generation_log.txt

Step 1

,

,

,

, |, 

,

,


chosen=

|entropy=1.077|T=0.6|K=500
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Step 2
Probability,Probability,From,Let,Probability,By,In,##
chosen=In|entropy=2.033|T=0.6|K=500
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Step 3
 this, the, many, this, the, the, this, my
chosen= this|entropy=0.897|T=0.6|K=500
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Step 4
 chapter, chapter, chapter, chapter, chapter, Chapter, chapter, chapter
chosen= chapter|entropy=0.009|T=0.6|K=500
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Step 5
,,,, we,,,,,,,,,,
chosen=,|entropy=0.044|T=0.6|K=500
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[Evaluator after step 5]: GOOD
Step 6
 we, we, we, I, we, they, we, we
chosen= we|entropy=0.241|T=0.6|K=500
----------------------------------------
Step 7
 will, describe, dive, unravel, embark,'ll, will, will
chosen= will|entropy=1.617|T=0.6|K=500
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Step 8
 delve, explore, study, travel, focus, carefully, explore, explore
chosen= explore|entropy=0.767|T=0.6|K=500
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Step 9
 the, a, the, the, the, rigorous, the, the
chosen= the|entropy=0.140|T=0.6|K=500
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Step 10
 concept, deep, fundamental, intricate, fundamental, elegant, fundamental, fundamentals
chosen= fundamental|entropy=1.100|T=0.6|K=500
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[Evaluator after step 10]: GOOD
Step 11
 aspects, concepts, concepts, aspects, principles, concepts, concepts, principles
chosen= concepts|entropy=0.534|T=0.6|K=500
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Step 12
 of, of, and, of, of, and, of, of
chosen= of|entropy=0.714|T=0.6|K=500
----------------------------------------
Step 13
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 14
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.025|T=0.6|K=500
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Step 15
,, and,.,,, in,,,,, and
chosen=,|entropy=0.982|T=0.6|K=500
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[Evaluator after step 15]: GOOD
Step 16
 focusing, focusing, particularly, starting, which, examining, focusing, which
chosen= focusing|entropy=0.768|T=0.6|K=500
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Step 17
 on, on, on, on, on, on, on, on
chosen= on|entropy=0.004|T=0.6|K=500
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Step 18
 its, its, its, the, deep, subsets, its, deep
chosen= its|entropy=0.914|T=0.6|K=500
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Step 19
 deep, deep, governing, mathematical, deep, depth, mathematical, deep
chosen= mathematical|entropy=0.974|T=0.6|K=500
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Step 20
 structure, structure, under, under, depth, basis, structure, representation
chosen= structure|entropy=1.188|T=0.6|K=500
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[Evaluator after step 20]: GOOD
Step 21
 and, and, and, and, and,,, and,,
chosen= and|entropy=0.579|T=0.6|K=500
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Step 22
 how, how, the, intric, how, the, its, application
chosen= its|entropy=1.574|T=0.6|K=500
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Step 23
 applications, deep, deep, applications, applications, connections, applications, applications
chosen= applications|entropy=1.104|T=0.6|K=500
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Step 24
 in,., in,.,., to, in,.
chosen= in|entropy=0.820|T=0.6|K=500
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Step 25
 various, various, various, decision, real, poetry, various, various
chosen= various|entropy=0.393|T=0.6|K=500
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[Evaluator after step 25]: GOOD
Step 26
 fields, contexts, domains, fields, fields, subsets, fields, fields
chosen= fields|entropy=0.561|T=0.6|K=500
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Step 27
.,., such,.,.,.,.,.
chosen=.|entropy=0.517|T=0.6|K=500
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Step 28
 Probability, Probability, We, Probability, Probability, Probability, Probability, Our
chosen= Probability|entropy=0.763|T=0.6|K=500
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Step 29
 theory, theory, is, theory, theory, probability, theory, theory
chosen= theory|entropy=0.104|T=0.6|K=500
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Step 30
 is, is, is,,, is, is, is, is
chosen= is|entropy=0.422|T=0.6|K=500
----------------------------------------
[Evaluator after step 30]: GOOD
Step 31
 a, a, a, a, a, a, a, a
chosen= a|entropy=0.345|T=0.6|K=500
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Step 32
 fundamental, branch, powerful, multid, branch, fascinating, branch, cornerstone
chosen= branch|entropy=1.142|T=0.6|K=500
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Step 33
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
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Step 34
 mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics
chosen= mathematics|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 35
 that, that, that, that, that, concerned, that, that
chosen= that|entropy=0.042|T=0.6|K=500
----------------------------------------
[Evaluator after step 35]: GOOD
Step 36
 deals, deals, deals, deals, deals, deals, deals, deals
chosen= deals|entropy=0.109|T=0.6|K=500
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Step 37
 with, with, with, with, with, with, with, with
chosen= with|entropy=0.001|T=0.6|K=500
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Step 38
 the, the, the, the, the, harness, the, the
chosen= the|entropy=0.038|T=0.6|K=500
----------------------------------------
Step 39
 study, analysis, probability, modeling, analysis, measurement, modeling, modeling
chosen= modeling|entropy=1.323|T=0.6|K=500
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Step 40
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.125|T=0.6|K=500
----------------------------------------
[Evaluator after step 40]: GOOD
Step 41
 random, random, random, random, random, random, random, random
chosen= random|entropy=0.053|T=0.6|K=500
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Step 42
 phenomena, phenomena, phenomena, phenomena, phenomena, phenomena, phenomena, phenomena
chosen= phenomena|entropy=0.300|T=0.6|K=500
----------------------------------------
Step 43
,,,,.,.,.,., and,.
chosen= and|entropy=1.114|T=0.6|K=500
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Step 44
 the, the, the, distributions, the, its, the, the
chosen= the|entropy=0.118|T=0.6|K=500
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Step 45
 analysis, analysis, analysis, analysis, analysis, analysis, study, computation
chosen= study|entropy=0.632|T=0.6|K=500
----------------------------------------
[Evaluator after step 45]: GOOD
Step 46
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
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Step 47
 outcomes, their, random, probability, the, their, probabilities, probabilities
chosen= probabilities|entropy=1.563|T=0.6|K=500
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Step 48
 associated, associated, of, associated, of, latent, associated, of
chosen= associated|entropy=0.756|T=0.6|K=500
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Step 49
 with, with, with, with, with, or, with, with
chosen= with|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 50
 these, those, those, those, them, them, those, them
chosen= those|entropy=1.238|T=0.6|K=500
----------------------------------------
[Evaluator after step 50]: GOOD
Step 51
 phenomena, phenomena, phenomena, exhibits, phenomena, events, phenomena, phenomena
chosen= phenomena|entropy=0.237|T=0.6|K=500
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Step 52
.,.,.,.,.,.,.,.
chosen=.|entropy=0.041|T=0.6|K=500
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Step 53
 It, It, The, It, It, Here, It, It
chosen= It|entropy=0.158|T=0.6|K=500
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Step 54
 is, provides, is,'s, forms, provides, is, forms
chosen= is|entropy=0.851|T=0.6|K=500
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Step 55
 a, essential, a, used, foundational, fundamental, a, built
chosen= a|entropy=0.648|T=0.6|K=500
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[Evaluator after step 55]: GOOD
Step 56
 crucial, powerful, widely, logical, foundational, tool, powerful, cornerstone
chosen= powerful|entropy=0.978|T=0.6|K=500
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Step 57
 tool, tool, tool, tool, tool, tool, tool, tool
chosen= tool|entropy=0.012|T=0.6|K=500
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Step 58
 that, used, in, for, for, used, for, for
chosen= for|entropy=1.271|T=0.6|K=500
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Step 59
 understanding, understanding, understanding, understanding, analyzing, understanding, understanding, understanding
chosen= understanding|entropy=0.285|T=0.6|K=500
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Step 60
 and, and, and, the, the, and, and, and
chosen= and|entropy=0.079|T=0.6|K=500
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[Evaluator after step 60]: GOOD
Step 61
 analyzing, predicting, analyzing, analyzing, analyzing, explaining, predicting, analyzing
chosen= predicting|entropy=0.664|T=0.6|K=500
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Step 62
 outcomes, outcomes, the, outcomes, the, outcomes, outcomes, outcomes
chosen= outcomes|entropy=0.801|T=0.6|K=500
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Step 63
 of, in, in, in, of,.

, that, in
chosen= that|entropy=0.853|T=0.6|K=500
----------------------------------------
Step 64
 are, are, are, are, are, cannot, are, are
chosen= are|entropy=0.037|T=0.6|K=500
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Step 65
 uncertain, uncertain, influenced, influenced, not, based, uncertain, uncertain
chosen= uncertain|entropy=0.654|T=0.6|K=500
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[Evaluator after step 65]: GOOD
Step 66
.

, and,.,., and,.

, or,.


chosen= or|entropy=1.028|T=0.6|K=500
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Step 67
 depend, random, complex, variable, probabil, probabil, variable, probabil
chosen= variable|entropy=1.071|T=0.6|K=500
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Step 68
 in, in, in, in, in,,,.

,.


chosen=.

|entropy=1.190|T=0.6|K=500
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Step 69
First,The,The,To,In,In,The,This
chosen=The|entropy=1.592|T=0.6|K=500
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Step 70
 chapter, chapter, chapter, beginning, chapter, enduring, chapter, chapter
chosen= chapter|entropy=0.033|T=0.6|K=500
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[Evaluator after step 70]: GOOD
Step 71
 begins, begins, will, will, will, begins, will, will
chosen= will|entropy=0.613|T=0.6|K=500
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Step 72
 start, cover, start, commence, start, begin, cover, cover
chosen= cover|entropy=1.091|T=0.6|K=500
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Step 73
 topics, the, key, the, the, topics, the, several
chosen= the|entropy=0.880|T=0.6|K=500
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Step 74
 basic, main, following, basics, basics, basic, basic, basic
chosen= basic|entropy=0.812|T=0.6|K=500
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Step 75
 concepts, elements, principles, foundations, principles, definition, definitions, concepts
chosen= definitions|entropy=1.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 75]: GOOD
Step 76
 and, and, of,,, of, and, and, and
chosen= and|entropy=0.649|T=0.6|K=500
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Step 77
 properties, concepts, properties, properties, concepts, governing, concepts, concepts
chosen= concepts|entropy=1.162|T=0.6|K=500
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Step 78
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.108|T=0.6|K=500
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Step 79
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
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Step 80
,,,,,,,,,, theory,,, theory
chosen=,|entropy=0.554|T=0.6|K=500
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[Evaluator after step 80]: GOOD
Step 81
 such, including, including, including, including, probabil, such, including
chosen= such|entropy=0.549|T=0.6|K=500
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Step 82
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.7|K=200
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Step 83
 the, events, sample, basic, the, probability, the, what
chosen= the|entropy=1.403|T=0.6|K=500
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Step 84
 probability, sample, probability, definition, probability, probability, probability, probability
chosen= probability|entropy=0.808|T=0.6|K=500
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Step 85
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.040|T=0.6|K=500
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[Evaluator after step 85]: GOOD
Step 86
 an, an, an, an, an, an, an, an
chosen= an|entropy=0.040|T=0.6|K=500
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Step 87
 event, outcome, event, event, event, event, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 88
,,,,,,,,,,,,,,,
chosen=,|entropy=0.334|T=0.6|K=500
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Step 89
 the, the, the, the, probability, how, the, the
chosen= the|entropy=0.023|T=0.6|K=500
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Step 90
 probability, probability, concept, probability, probability, risk, probability, union
chosen= probability|entropy=0.139|T=0.6|K=500
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[Evaluator after step 90]: GOOD
Step 91
 of, distribution, of, space, of, versus, distribution, distribution
chosen= distribution|entropy=0.623|T=0.6|K=500
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Step 92
,,,, functions,,,,,,,,,,
chosen=,|entropy=0.310|T=0.6|K=500
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Step 93
 and, and, and, and, the, subjective, and, and
chosen= and|entropy=0.231|T=0.6|K=500
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Step 94
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.007|T=0.6|K=500
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Step 95
 probability, probability, central, probability, concept, random, probability, joint
chosen= probability|entropy=1.072|T=0.6|K=500
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[Evaluator after step 95]: GOOD
Step 96
 of, of, of, of, of, of, of, measure
chosen= of|entropy=0.305|T=0.6|K=500
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Step 97
 multiple, multiple, events, a, dependent, the, multiple, multiple
chosen= multiple|entropy=0.831|T=0.6|K=500
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Step 98
 events, events, events, events, events, events, events, outcomes
chosen= events|entropy=0.011|T=0.6|K=500
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Step 99
.,., occurring,.,.,,,.,.
chosen=.|entropy=0.313|T=0.6|K=500
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Step 100
 It, It, It, We, It, We, It, We
chosen= It|entropy=0.625|T=0.6|K=500
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[Evaluator after step 100]: GOOD
Step 101
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.001|T=0.6|K=500
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Step 102
 also, also, also,also, also, also, also, also
chosen= also|entropy=0.008|T=0.6|K=500
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Step 103
 introduce, discuss, discuss, provide, introduce, touch, delve, cover
chosen= delve|entropy=1.325|T=0.6|K=500
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Step 104
 into, into, into, into, into, into, into, into
chosen= into|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 105
 the, the, the, advanced, the, further, the, the
chosen= the|entropy=0.312|T=0.6|K=500
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[Evaluator after step 105]: GOOD
Step 106
 concepts, mathematical, mathematical, theoretical, more, mathematical, mathematical, foundational
chosen= mathematical|entropy=0.963|T=0.6|K=500
----------------------------------------
Step 107
 representations, properties, foundations, tools, structure, foundation, foundations, foundations
chosen= foundations|entropy=1.979|T=0.6|K=500
----------------------------------------
Step 108
 of, of, of, of, of, that, of,,
chosen= of|entropy=0.250|T=0.6|K=500
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Step 109
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.002|T=0.6|K=500
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Step 110
,,,,,, theory, theory, theory,,, theory
chosen=,|entropy=0.694|T=0.6|K=500
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[Evaluator after step 110]: GOOD
Step 111
 including, including, including, including, such, including, including, including
chosen= including|entropy=0.175|T=0.6|K=500
----------------------------------------
Step 112
 measure, the, concepts, probability, the, although, concepts, the
chosen= concepts|entropy=0.871|T=0.6|K=500
----------------------------------------
Step 113
 like, like, such, like, like, such, such, such
chosen= such|entropy=0.585|T=0.6|K=500
----------------------------------------
Step 114
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 115
 probability, sample, stochastic, add, probability, ax, measure, expectation
chosen= measure|entropy=1.926|T=0.6|K=500
----------------------------------------
[Evaluator after step 115]: GOOD
Step 116
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.028|T=0.6|K=500
----------------------------------------
Step 117
,,,,,,,, and,,,,,,
chosen=,|entropy=0.426|T=0.6|K=500
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Step 118
 stochastic, stochastic, caus, stochastic, probability, calculus, stochastic, conditional
chosen= stochastic|entropy=0.920|T=0.6|K=500
----------------------------------------
Step 119
 processes, processes, processes, processes, processes, processes, processes, processes
chosen= processes|entropy=0.053|T=0.6|K=500
----------------------------------------
Step 120
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 120]: GOOD
Step 121
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.001|T=0.6|K=500
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Step 122
 the, mathematical, random, stochastic, probability, mathematical, conditional, conditional
chosen= conditional|entropy=1.620|T=0.6|K=500
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Step 123
 probabilities, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.055|T=0.6|K=500
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Step 124
.,.,.,.,.

,.

,.

,.


chosen=.

|entropy=0.478|T=0.6|K=500
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Step 125
Throughout,The,Some,Additionally,Additionally,Additional,The,Integration
chosen=The|entropy=2.037|T=0.6|K=500
----------------------------------------
[Evaluator after step 125]: GOOD
Step 126
 application, language, chapter, chapter, chapter, chapter, chapter, chapter
chosen= chapter|entropy=0.121|T=0.6|K=500
----------------------------------------
Step 127
 will, will, will, will, will, is, will, will
chosen= will|entropy=0.208|T=0.6|K=500
----------------------------------------
Step 128
 conclude, provide, also, help, provide, provide, also, also
chosen= also|entropy=0.998|T=0.6|K=500
----------------------------------------
Step 129
 introduce, touch, explore, discuss, discuss, have, touch, discuss
chosen= touch|entropy=1.420|T=0.6|K=500
----------------------------------------
Step 130
 upon, upon, upon, upon, upon, on, upon, on
chosen= upon|entropy=0.544|T=0.6|K=500
----------------------------------------
[Evaluator after step 130]: GOOD
Step 131
 the, the, the, important, the, basic, the, the
chosen= the|entropy=0.503|T=0.6|K=500
----------------------------------------
Step 132
 importance, applications, application, interpretation, three, importance, applications, applications
chosen= applications|entropy=1.504|T=0.6|K=500
----------------------------------------
Step 133
 of, of, of, of, of, of, of, areas
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 134
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 135
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.196|T=0.6|K=500
----------------------------------------
[Evaluator after step 135]: GOOD
Step 136
 in, in, in, in, in, in, in, in
chosen= in|entropy=0.025|T=0.6|K=500
----------------------------------------
Step 137
 various, various, various, real, various, physics, real, various
chosen= real|entropy=0.953|T=0.6|K=500
----------------------------------------
Step 138
-world,-world,-life,-world,-world,-world,-world,-world
chosen=-world|entropy=0.529|T=0.6|K=500
----------------------------------------
Step 139
 scenarios, situations, scenarios, scenarios, scenarios, scenarios, scenarios, scenarios
chosen= scenarios|entropy=0.276|T=0.6|K=500
----------------------------------------
Step 140
,,,,,,,,,,,,,,,
chosen=,|entropy=0.050|T=0.6|K=500
----------------------------------------
[Evaluator after step 140]: GOOD
Step 141
 such, such, such, such, such, including, such, such
chosen= such|entropy=0.070|T=0.6|K=500
----------------------------------------
Step 142
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 143
 in, data, risk, decision, statistical, in, in, in
chosen= in|entropy=1.242|T=0.6|K=500
----------------------------------------
Step 144
 finance, statistics, statistics, finance, statistics, machine, finance, statistics
chosen= finance|entropy=0.872|T=0.6|K=500
----------------------------------------
Step 145
,,,,,,,,,,,,,,,
chosen=,|entropy=0.019|T=0.6|K=500
----------------------------------------
[Evaluator after step 145]: GOOD
Step 146
 statistics, statistics, science, computer, statistics, mathematics, healthcare, computer
chosen= healthcare|entropy=1.654|T=0.6|K=500
----------------------------------------
Step 147
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 148
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.081|T=0.6|K=500
----------------------------------------
Step 149
 other, engineering, other, decision, other, scientific, engineering, machine
chosen= engineering|entropy=1.635|T=0.6|K=500
----------------------------------------
Step 150
.,.,.,.,.,.,.,.
chosen=.|entropy=0.184|T=0.6|K=500
----------------------------------------
[Evaluator after step 150]: GOOD
Step 151
 It, It, Understanding, It, We, It, It, It
chosen= It|entropy=1.614|T=0.6|K=500
----------------------------------------
Step 152
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.007|T=0.6|K=500
----------------------------------------
Step 153
 help, introduce, discuss, analyze, discuss, be, provide, highlight
chosen= provide|entropy=1.799|T=0.6|K=500
----------------------------------------
Step 154
 an, practical, an, an, an, guidelines, an, an
chosen= an|entropy=0.600|T=0.6|K=500
----------------------------------------
Step 155
 overview, overview, overview, overview, understanding, understanding, overview, overview
chosen= overview|entropy=0.419|T=0.6|K=500
----------------------------------------
[Evaluator after step 155]: GOOD
Step 156
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 157
 the, the, the, key, the, the, the, the
chosen= the|entropy=0.845|T=0.6|K=500
----------------------------------------
Step 158
 principles, different, key, principles, techniques, basic, statistical, mathematics
chosen= statistical|entropy=2.338|T=0.6|K=500
----------------------------------------
Step 159
 models, methods, methods, limits, models, techniques, methods, models
chosen= methods|entropy=0.563|T=0.6|K=500
----------------------------------------
Step 160
 used, used, used, used, used, and, used, used
chosen= used|entropy=0.212|T=0.6|K=500
----------------------------------------
[Evaluator after step 160]: GOOD
Step 161
 in, in, in, in, in, in, in, in
chosen= in|entropy=0.198|T=0.6|K=500
----------------------------------------
Step 162
 probability, probability, probability, probability, probability, these, probability, probability
chosen= probability|entropy=0.438|T=0.6|K=500
----------------------------------------
Step 163
,,,, theory, theory,,, theory, theory,,
chosen= theory|entropy=0.824|T=0.6|K=500
----------------------------------------
Step 164
,,,,,,,, and,,,,,,
chosen=,|entropy=0.472|T=0.6|K=500
----------------------------------------
Step 165
 including, such, including, including, including, including, including, including
chosen= including|entropy=0.521|T=0.6|K=500
----------------------------------------
[Evaluator after step 165]: GOOD
Step 166
 the, hypothesis, hypothesis, hypothesis, techniques, probability, hypothesis, hypothesis
chosen= hypothesis|entropy=1.053|T=0.6|K=500
----------------------------------------
Step 167
 testing, testing, testing, testing, testing, testing, testing, testing
chosen= testing|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 168
,, and, and,,, and, and, and, and
chosen= and|entropy=0.617|T=0.6|K=500
----------------------------------------
Step 169
 confidence, the, goodness, confidence, statistical, confidence, confidence, confidence
chosen= confidence|entropy=0.766|T=0.6|K=500
----------------------------------------
Step 170
 intervals, intervals, intervals, intervals, intervals, intervals, intervals, intervals
chosen= intervals|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 170]: GOOD
Step 171
.

,.,.

, and,.,.

,.

,.


chosen=.

|entropy=0.546|T=0.6|K=500
----------------------------------------
Step 172
In,In,The,Safety,Throughout,Each,In,In
chosen=In|entropy=1.820|T=0.6|K=500
----------------------------------------
Step 173
 addition, addition, addition, addition, conclusion, addition, addition, addition
chosen= addition|entropy=0.330|T=0.6|K=500
----------------------------------------
Step 174
 to,,, to, to,,,,, to,,
chosen= to|entropy=0.686|T=0.6|K=500
----------------------------------------
Step 175
 the, the, its, the, the, the, the, the
chosen= the|entropy=0.638|T=0.6|K=500
----------------------------------------
[Evaluator after step 175]: GOOD
Step 176
 mathematical, mathematical, theoretical, theoretical, mathematical, material, mathematical, theoretical
chosen= mathematical|entropy=0.487|T=0.6|K=500
----------------------------------------
Step 177
 foundations, aspects, content, theory, concepts, information, content, foundations
chosen= content|entropy=1.625|T=0.6|K=500
----------------------------------------
Step 178
,,,,,,,,,,,,,,,
chosen=,|entropy=0.017|T=0.6|K=500
----------------------------------------
Step 179
 the, the, this, the, the, we, the, the
chosen= the|entropy=0.487|T=0.6|K=500
----------------------------------------
Step 180
 chapter, chapter, chapter, chapter, chapter, chapter, chapter, chapter
chosen= chapter|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 180]: GOOD
Step 181
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 182
 also, also, also, also, touch, discuss, also, include
chosen= also|entropy=0.330|T=0.6|K=500
----------------------------------------
Step 183
 include, discuss, touch, cover, provide, break, touch, emphasize
chosen= touch|entropy=1.906|T=0.6|K=500
----------------------------------------
Step 184
 upon, upon, upon, upon, upon, on, upon, upon
chosen= upon|entropy=0.372|T=0.6|K=500
----------------------------------------
Step 185
 the, the, the, the, the, some, the, the
chosen= the|entropy=0.085|T=0.6|K=500
----------------------------------------
[Evaluator after step 185]: GOOD
Step 186
 broader, theoretical, importance, importance, wider, evolution, importance, practical
chosen= importance|entropy=1.764|T=0.6|K=500
----------------------------------------
Step 187
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.025|T=0.6|K=500
----------------------------------------
Step 188
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.007|T=0.6|K=500
----------------------------------------
Step 189
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.150|T=0.6|K=500
----------------------------------------
Step 190
 in, in, in, in, in, in, in, and
chosen= in|entropy=0.030|T=0.6|K=500
----------------------------------------
[Evaluator after step 190]: GOOD
Step 191
 various, both, modern, various, shaping, higher, various, making
chosen= various|entropy=1.785|T=0.6|K=500
----------------------------------------
Step 192
 scientific, disciplines, standardized, areas, disciplines, disciplines, fields, domains
chosen= fields|entropy=1.234|T=0.6|K=500
----------------------------------------
Step 193
,,,,,,., of, this, and,,
chosen= and|entropy=0.649|T=0.6|K=500
----------------------------------------
Step 194
 its, its, how, its, its, its, its, its
chosen= its|entropy=0.119|T=0.6|K=500
----------------------------------------
Step 195
 impact, impact, role, role, implications, implication, impact, continued
chosen= impact|entropy=1.525|T=0.6|K=500
----------------------------------------
[Evaluator after step 195]: GOOD
Step 196
 on, on, on, on, on, on, on, on
chosen= on|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 197
 modern, the, scientific, different, technological, modern, scientific, the
chosen= scientific|entropy=1.792|T=0.6|K=500
----------------------------------------
Step 198
 research, research, discovery, discovery, research, conduct, research, inquiry
chosen= research|entropy=0.310|T=0.6|K=500
----------------------------------------
Step 199
 and,., and, and, and,., and, and
chosen= and|entropy=0.486|T=0.6|K=500
----------------------------------------
Step 200
 innovation, decision, technological, education, innovation, development, decision, technological
chosen= decision|entropy=1.475|T=0.6|K=500
----------------------------------------
[Evaluator after step 200]: GOOD
Step 201
-making,-making,-making,-making,-making,-making,-making,-making
chosen=-making|entropy=0.016|T=0.6|K=500
----------------------------------------
Step 202
.,.

,., processes,.

, processes,.,.
chosen=.|entropy=1.090|T=0.6|K=500
----------------------------------------
Step 203
 This, It, It, It, Probability, It, It, The
chosen= It|entropy=0.361|T=0.6|K=500
----------------------------------------
Step 204
 will, will, will, will, will, provides, will, will
chosen= will|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 205
 emphasize, emphasize, emphasize, emphasize, emphasize, mention, encourage, also
chosen= encourage|entropy=1.503|T=0.6|K=500
----------------------------------------
[Evaluator after step 205]: GOOD
Step 206
 students, students, students, critical, the, readers, readers, readers
chosen= readers|entropy=1.075|T=0.6|K=500
----------------------------------------
Step 207
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 208
 explore, develop, understand, think, explore, explore, explore, understand
chosen= explore|entropy=1.086|T=0.6|K=500
----------------------------------------
Step 209
 the, further, the, and, and, the, the, further
chosen= the|entropy=0.719|T=0.6|K=500
----------------------------------------
Step 210
 rich, possibilities, possibilities, deeper, possibilities, mathematics, mathematical, concepts
chosen= mathematical|entropy=2.221|T=0.6|K=500
----------------------------------------
[Evaluator after step 210]: GOOD
Step 211
 under, and, content, side, concepts, depths, structure, structure
chosen= structure|entropy=1.875|T=0.6|K=500
----------------------------------------
Step 212
 and, and, of, of, and, of, of, of
chosen= of|entropy=0.741|T=0.6|K=500
----------------------------------------
Step 213
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 214
 theory, theory, theory, theory, theory, by, theory, theory
chosen= theory|entropy=0.214|T=0.6|K=500
----------------------------------------
Step 215
 further, and,,,,, further, and, and, and
chosen= and|entropy=0.341|T=0.6|K=500
----------------------------------------
[Evaluator after step 215]: GOOD
Step 216
 its, its, its, appreciate, its, its, its, the
chosen= its|entropy=0.191|T=0.6|K=500
----------------------------------------
Step 217
 relevance, relevance, various, real, potential, implications, relevance, applications
chosen= relevance|entropy=1.404|T=0.6|K=500
----------------------------------------
Step 218
 in, to, in, in, in, in, in, to
chosen= in|entropy=0.694|T=0.6|K=500
----------------------------------------
Step 219
 everyday, different, their, their, modern, their, their, modern
chosen= their|entropy=1.853|T=0.6|K=500
----------------------------------------
Step 220
 own, own, own, own, own, own, own, own
chosen= own|entropy=0.151|T=0.6|K=500
----------------------------------------
[Evaluator after step 220]: GOOD
Step 221
 lives, lives, lives, domains, studies, lives, lives, life
chosen= lives|entropy=0.558|T=0.6|K=500
----------------------------------------
Step 222
.

,.

,.

,.

,.

, to,.

,.


chosen=.

|entropy=0.062|T=0.6|K=500
----------------------------------------
Step 223
The,The,I,It,Throughout,One,We,Throughout
chosen=We|entropy=1.907|T=0.6|K=500
----------------------------------------
Step 224
 will, will, will, will, will, suggest, will, will
chosen= will|entropy=0.095|T=0.6|K=500
----------------------------------------
Step 225
 also, conclude, also, end, also, not, also, end
chosen= also|entropy=1.563|T=0.6|K=500
----------------------------------------
[Evaluator after step 225]: GOOD
Step 226
 provide, look, mention, include, discuss, have, provide, present
chosen= provide|entropy=2.213|T=0.6|K=500
----------------------------------------
Step 227
 an, an, a, examples, an, some, some, an
chosen= some|entropy=1.292|T=0.6|K=500
----------------------------------------
Step 228
 exercises, examples, examples, read, resources, notation, examples, examples
chosen= examples|entropy=1.079|T=0.6|K=500
----------------------------------------
Step 229
 and, and, and, and, and, of, and, and
chosen= and|entropy=0.586|T=0.6|K=500
----------------------------------------
Step 230
 exercises, exercises, exercises, exercises, exercises, engaging, exercises, cases
chosen= exercises|entropy=0.795|T=0.6|K=500
----------------------------------------
[Evaluator after step 230]: GOOD
Step 231
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.059|T=0.6|K=500
----------------------------------------
Step 232
 help, solid, illustrate, help, help, reinforce, help, reinforce
chosen= help|entropy=1.090|T=0.6|K=500
----------------------------------------
Step 233
 reinforce, reinforce, reinforce, students, reinforce, guide, reinforce, readers
chosen= reinforce|entropy=0.379|T=0.6|K=500
----------------------------------------
Step 234
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.014|T=0.6|K=500
----------------------------------------
Step 235
 concepts, concepts, concepts, understanding, concepts, concepts, concepts, concepts
chosen= concepts|entropy=0.110|T=0.6|K=500
----------------------------------------
[Evaluator after step 235]: GOOD
Step 236
 discussed, discussed, learned, discussed, and,.

, discussed, learned
chosen= discussed|entropy=0.657|T=0.6|K=500
----------------------------------------
Step 237
 in,.

,., in, throughout,., in, in
chosen= in|entropy=0.360|T=0.6|K=500
----------------------------------------
Step 238
 the, the, the, the, the, this, the, the
chosen= the|entropy=0.209|T=0.6|K=500
----------------------------------------
Step 239
 chapter, chapter, chapter, chapter, chapter, chapter, chapter, chapter
chosen= chapter|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 240
.,.,.,.

,.,.

,.,.


chosen=.|entropy=0.561|T=0.6|K=500
----------------------------------------
[Evaluator after step 240]: GOOD
Step 241
 The, The, The, Finally, By, In, The, The
chosen= The|entropy=0.855|T=0.6|K=500
----------------------------------------
Step 242
 chapter, inclusion, chapter, willingness, chapter, topics, chapter, chapter
chosen= chapter|entropy=0.703|T=0.6|K=500
----------------------------------------
Step 243
 is, is, is, is, is, will, is, will
chosen= is|entropy=0.745|T=0.6|K=500
----------------------------------------
Step 244
 structured, designed, structured, expected, structured, designed, designed, structured
chosen= designed|entropy=0.729|T=0.6|K=500
----------------------------------------
Step 245
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 245]: GOOD
Step 246
 be, be, be, provide, be, take, be, be
chosen= be|entropy=0.115|T=0.6|K=500
----------------------------------------
Step 247
 an, a, a, a, a, educational, comprehensive, engaging
chosen= comprehensive|entropy=1.742|T=0.6|K=500
----------------------------------------
Step 248
 but,,,,, and,,, and, and, and
chosen= and|entropy=0.375|T=0.6|K=500
----------------------------------------
Step 249
 informative, will, informative, challenging, to, engaging, engaging, explor
chosen= engaging|entropy=1.662|T=0.6|K=500
----------------------------------------
Step 250
,,,,,,,, for,,,,,,
chosen=,|entropy=0.164|T=0.6|K=500
----------------------------------------
[Evaluator after step 250]: GOOD
Step 251
 making, providing, allowing, allowing, providing, inviting, with, covering
chosen= with|entropy=1.852|T=0.6|K=500
----------------------------------------
Step 252
 a, a, a, a, a, both, a, a
chosen= a|entropy=0.148|T=0.6|K=500
----------------------------------------
Step 253
 balance, focus, balance, clear, balance, clear, focus, focus
chosen= focus|entropy=0.958|T=0.6|K=500
----------------------------------------
Step 254
 on, on, on, on, on, on, on, on
chosen= on|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 255
 both, understanding, the, both, both, deep, the, building
chosen= the|entropy=1.256|T=0.6|K=500
----------------------------------------
[Evaluator after step 255]: GOOD
Step 256
 mathematical, mathematical, mathematical, mathematical, deep, visualization, mathematical, mathematical
chosen= mathematical|entropy=0.183|T=0.6|K=500
----------------------------------------
Step 257
 principles, foundations, and, rigor, foundations, and, foundations, aspects
chosen= foundations|entropy=1.668|T=0.6|K=500
----------------------------------------
Step 258
 and, and, and, and, and, of, and, and
chosen= and|entropy=0.396|T=0.6|K=500
----------------------------------------
Step 259
 applications, applications, applications, applications, applications, their, applications, applications
chosen= applications|entropy=0.475|T=0.6|K=500
----------------------------------------
Step 260
.

, of, of, of, of, of, of, of
chosen= of|entropy=0.322|T=0.6|K=500
----------------------------------------
[Evaluator after step 260]: GOOD
Step 261
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 262
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.013|T=0.6|K=500
----------------------------------------
Step 263
.

,.

,.

,.

,.

,.,.

,.

chosen=.

|entropy=0.052|T=0.6|K=500
----------------------------------------
Step 264
The,This,Through,For,By,You,The,Now
chosen=The|entropy=2.172|T=0.6|K=500
----------------------------------------
Step 265
 chapter, chapter, chapter, chapter, structure, summary, chapter, chapter
chosen= chapter|entropy=0.138|T=0.6|K=500
----------------------------------------
[Evaluator after step 265]: GOOD
Step 266
 is, is, is, leaves, is, is, will, closes
chosen= will|entropy=0.929|T=0.6|K=500
----------------------------------------
Step 267
 end, conclude, conclude, end, conclude, focus, conclude, conclude
chosen= conclude|entropy=0.868|T=0.6|K=500
----------------------------------------
Step 268
 with, with, with, with, with, with, by, by
chosen= by|entropy=0.482|T=0.6|K=500
----------------------------------------
Step 269
 summar, summar, summar, summar, summar, reviewing, summar, summar
chosen= summar|entropy=0.630|T=0.6|K=500
----------------------------------------
Step 270
izing,izing,izing,izing,izing,izing,izing,izing
chosen=izing|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 270]: GOOD
Step 271
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.012|T=0.6|K=500
----------------------------------------
Step 272
 key, key, key, key, key, main, key, main
chosen= key|entropy=0.355|T=0.6|K=500
----------------------------------------
Step 273
 concepts, concepts, ideas, concepts, concepts, topics, points, ideas
chosen= points|entropy=0.871|T=0.6|K=500
----------------------------------------
Step 274
 discussed, and, and, discussed, and, and, and, and
chosen= and|entropy=0.236|T=0.6|K=500
----------------------------------------
Step 275
 offering, emphasizing, emphasizing, emphasizing, presenting, helping, presenting, highlighting
chosen= presenting|entropy=1.347|T=0.6|K=500
----------------------------------------
[Evaluator after step 275]: GOOD
Step 276
 a, a, the, the, the, an, a, a
chosen= a|entropy=0.759|T=0.6|K=500
----------------------------------------
Step 277
 clear, clear, final, final, final, clear, clear, clear
chosen= clear|entropy=0.987|T=0.6|K=500
----------------------------------------
Step 278
 understanding,,, understanding, structure, and, and, understanding, structure
chosen= understanding|entropy=0.938|T=0.6|K=500
----------------------------------------
Step 279
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 280
 the, probability, probability, the, the, the, the, the
chosen= the|entropy=0.440|T=0.6|K=500
----------------------------------------
[Evaluator after step 280]: GOOD
Step 281
 mathematical, mathematical, mathematical, mathematical, mathematical, importance, fundamental, mathematical
chosen= fundamental|entropy=0.676|T=0.6|K=500
----------------------------------------
Step 282
 concepts, concepts, concepts, concepts, concepts, components, concepts, concepts
chosen= concepts|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 283
 of, of,.

, of, of, of, of, of
chosen= of|entropy=0.152|T=0.6|K=500
----------------------------------------
Step 284
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 285
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.005|T=0.6|K=500
----------------------------------------
[Evaluator after step 285]: GOOD
Step 286
.

,.

,.

,.
,.

,,,.

,.


chosen=.

|entropy=0.359|T=0.6|K=500
----------------------------------------
Step 287
The,It,I,By,This,First,I,One
chosen=I|entropy=2.021|T=0.6|K=500
----------------------------------------
Step 288
 hope, will,.,., hope, graduated, will, will
chosen= will|entropy=1.681|T=0.6|K=500
----------------------------------------
Step 289
 now, like, now, be, now, provide, be, use
chosen= be|entropy=0.785|T=0.6|K=500
----------------------------------------
Step 290
 writing, writing, adding, providing, discussing,joy, writing, in
chosen= writing|entropy=1.197|T=0.6|K=500
----------------------------------------
[Evaluator after step 290]: GOOD
Step 291
 a, this, this, the, this, an, this, this
chosen= this|entropy=0.263|T=0.6|K=500
----------------------------------------
Step 292
 chapter, chapter, chapter, chapter, chapter, chapter, chapter, chapter
chosen= chapter|entropy=0.028|T=0.6|K=500
----------------------------------------
Step 293
 in, as, in, under, for, along, in, in
chosen= in|entropy=1.129|T=0.6|K=500
----------------------------------------
Step 294
 a, English, a, a, a,-depth, a, Microsoft
chosen= a|entropy=0.776|T=0.6|K=500
----------------------------------------
Step 295
 more, clear, formal, scientific, way, primarily, formal, formal
chosen= formal|entropy=1.181|T=0.6|K=500
----------------------------------------
[Evaluator after step 295]: GOOD
Step 296
 and, academic, and, and, and, and, and, and
chosen= and|entropy=0.354|T=0.6|K=500
----------------------------------------
Step 297
 academic, academic, academic, comprehensive, rigorous, structured, academic, academic
chosen= academic|entropy=0.222|T=0.6|K=500
----------------------------------------
Step 298
 style, tone, tone, tone, tone, writing, tone, manner
chosen= tone|entropy=0.543|T=0.6|K=500
----------------------------------------
Step 299
,,,,,,,,,, for,,,,
chosen=,|entropy=0.041|T=0.6|K=500
----------------------------------------
Step 300
 with, ensuring, using, using, using, brushing, ensuring, following
chosen= ensuring|entropy=1.533|T=0.6|K=500
----------------------------------------
[Evaluator after step 300]: GOOD
Step 301
 that, that, that, that, that, that, that, that
chosen= that|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 302
 the, the, the, the, all, it, the, the
chosen= the|entropy=0.430|T=0.6|K=500
----------------------------------------
Step 303
 language, content, content, use, content, ideas, content, information
chosen= content|entropy=0.520|T=0.6|K=500
----------------------------------------
Step 304
 is, is, is, is, is, meets, is, is
chosen= is|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 305
 accurate, clear, well, clear, accurate, presented, both, appropriate
chosen= both|entropy=1.798|T=0.6|K=500
----------------------------------------
[Evaluator after step 305]: GOOD
Step 306
 comprehensive, informative, engaging, informative, informative, comprehensive, comprehensive, precise
chosen= comprehensive|entropy=1.435|T=0.6|K=500
----------------------------------------
Step 307
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 308
 insightful, suitable, structured, well, relevant, every, well, well
chosen= well|entropy=1.991|T=0.6|K=500
----------------------------------------
Step 309
-,-,-,-,-,-,-,-
chosen=-|entropy=0.054|T=0.6|K=500
----------------------------------------
Step 310
structured,structured,structured,structured,structured,organized,structured,structured
chosen=structured|entropy=0.086|T=0.6|K=500
----------------------------------------
[Evaluator after step 310]: GOOD
Step 311
.,.,.,.,.,.,.,.
chosen=.|entropy=0.945|T=0.6|K=500
----------------------------------------
Step 312
 I, The, I, The, We, The, I, I
chosen= I|entropy=0.802|T=0.6|K=500
----------------------------------------
Step 313
 will, will, will, will, am, will, will, will
chosen= will|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 314
 use, use, also, analyze, use, utilize, also, be
chosen= also|entropy=1.536|T=0.6|K=500
----------------------------------------
Step 315
 make, ensure, incorporate, provide, make, encourage, make, ensure
chosen= make|entropy=1.804|T=0.6|K=500
----------------------------------------
[Evaluator after step 315]: GOOD
Step 316
 sure, sure, sure, sure, sure, sure, sure, sure
chosen= sure|entropy=0.004|T=0.6|K=500
----------------------------------------
Step 317
 to, to, that, that, to, that, to, to
chosen= to|entropy=0.617|T=0.6|K=500
----------------------------------------
Step 318
 include, include, emphasize, present, include, provide, provide, provide
chosen= provide|entropy=1.318|T=0.6|K=500
----------------------------------------
Step 319
 clear, clear, as, clear, a, stepping, practical, explanations
chosen= practical|entropy=1.627|T=0.6|K=500
----------------------------------------
Step 320
 examples, examples, examples, examples, examples, insights, examples, applications
chosen= examples|entropy=0.352|T=0.6|K=500
----------------------------------------
[Evaluator after step 320]: GOOD
Step 321
 and, and, and, to, and, and, and, and
chosen= and|entropy=0.047|T=0.6|K=500
----------------------------------------
Step 322
 exercises, exercises, exercises, interactive, exercises, exercises, exercises, exercises
chosen= exercises|entropy=0.195|T=0.6|K=500
----------------------------------------
Step 323
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.348|T=0.6|K=500
----------------------------------------
Step 324
 enhance, enhance, assist, enhance, help, help, illustrate, help
chosen= illustrate|entropy=1.564|T=0.6|K=500
----------------------------------------
Step 325
 the, the, the, the, the, practical, the, the
chosen= the|entropy=0.020|T=0.6|K=500
----------------------------------------
[Evaluator after step 325]: GOOD
Step 326
 concepts, concepts, mathematical, concepts, concepts, theory, concepts, concepts
chosen= concepts|entropy=0.127|T=0.6|K=500
----------------------------------------
Step 327
 in, in, in,.

, and, and,.

,.
chosen=.

|entropy=1.645|T=0.6|K=500
----------------------------------------
Step 328
I,This,Evaluation,Who,The,References,I,I
chosen=I|entropy=1.895|T=0.6|K=500
----------------------------------------
Step 329
 hope, will, believe, must, want, understand, will, hope
chosen= will|entropy=1.182|T=0.6|K=500
----------------------------------------
Step 330
 avoid, be, also, check, also, structure, not, use
chosen= not|entropy=1.954|T=0.6|K=500
----------------------------------------
[Evaluator after step 330]: GOOD
Step 331
 use, make, use, use, use, use, use, discuss
chosen= use|entropy=0.839|T=0.6|K=500
----------------------------------------
Step 332
 any, markdown, any, any, markdown, any, any, any
chosen= any|entropy=0.388|T=0.6|K=500
----------------------------------------
Step 333
 markdown, markdown, markdown, markdown, markdown, technical, markdown, markdown
chosen= markdown|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 334
 formatting, formatting, but, or, formatting,.

, or, formatting
chosen= or|entropy=1.522|T=0.6|K=500
----------------------------------------
Step 335
 LaTeX, LaTeX, headings, LaTeX, LaTeX, outdated, formatting, LaTeX
chosen= formatting|entropy=0.796|T=0.6|K=500
----------------------------------------
[Evaluator after step 335]: GOOD
Step 336
,,,,,, to, for,,,,,,
chosen=,|entropy=1.101|T=0.6|K=500
----------------------------------------
Step 337
 and, and, but, and, just, and, but, adhere
chosen= but|entropy=0.999|T=0.6|K=500
----------------------------------------
Step 338
 I, instead, will, I, will, use, will, instead
chosen= will|entropy=1.339|T=0.6|K=500
----------------------------------------
Step 339
 use, present, utilize, use, present, Keep, write, use
chosen= write|entropy=0.751|T=0.6|K=500
----------------------------------------
Step 340
 it, the, the, the, the, the, in, the
chosen= in|entropy=0.527|T=0.6|K=500
----------------------------------------
[Evaluator after step 340]: GOOD
Step 341
 a, clear, a, plain, a, a, a, a
chosen= a|entropy=0.450|T=0.6|K=500
----------------------------------------
Step 342
 professional, clear, clear, conclusion, clear, clear, clear, clear
chosen= clear|entropy=0.346|T=0.6|K=500
----------------------------------------
Step 343
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.118|T=0.6|K=500
----------------------------------------
Step 344
 concise, concise, concise, concise, concise, concise, concise, concise
chosen= concise|entropy=0.327|T=0.6|K=500
----------------------------------------
Step 345
 manner, manner, manner, manner, manner, manner, manner, manner
chosen= manner|entropy=0.223|T=0.6|K=500
----------------------------------------
[Evaluator after step 345]: GOOD
Step 346
.

,,,.

,.,,,.
,,,,
chosen=,|entropy=1.448|T=0.6|K=500
----------------------------------------
Step 347
 as, using, as, using, with, covering, with, with
chosen= with|entropy=0.942|T=0.6|K=500
----------------------------------------
Step 348
 appropriate, appropriate, paragraph, appropriate, each, some, appropriate, clear
chosen= appropriate|entropy=0.472|T=0.6|K=500
----------------------------------------
Step 349
 headings, headings, headings, problem, headings, sections, headings, headings
chosen= headings|entropy=0.153|T=0.6|K=500
----------------------------------------
Step 350
 and, and, and, and, and, to, and, and
chosen= and|entropy=0.024|T=0.6|K=500
----------------------------------------
[Evaluator after step 350]: GOOD
Step 351
 sub, sections, sub, sub, sections, subsection, sections, sub
chosen= sections|entropy=0.401|T=0.6|K=500
----------------------------------------
Step 352
,, to, as, as, as,.

,.

, as
chosen=.

|entropy=1.606|T=0.6|K=500
----------------------------------------
Step 353
The,**,I,This,The,(W,Now,This
chosen=Now|entropy=1.754|T=0.6|K=500
----------------------------------------
Step 354
,,,,,,,,,,,,,,,
chosen=,|entropy=0.162|T=0.6|K=500
----------------------------------------
Step 355
 let, I, I, the, let, student, let, let
chosen= let|entropy=0.800|T=0.6|K=500
----------------------------------------
[Evaluator after step 355]: GOOD
Step 356
's,'s, me,'s,'s, me, me,'s
chosen= me|entropy=0.642|T=0.6|K=500
----------------------------------------
Step 357
 write, read, begins, think, write, approach, proceed, start
chosen= proceed|entropy=0.745|T=0.6|K=500
----------------------------------------
Step 358
 to, with,.
, to, to, to, with, to
chosen= with|entropy=0.315|T=0.6|K=500
----------------------------------------
Step 359
 the, the, the, the, writing, writing, writing, the
chosen= writing|entropy=0.700|T=0.6|K=500
----------------------------------------
Step 360
 this, the, the, the, this, the, the, the
chosen= the|entropy=0.545|T=0.6|K=500
----------------------------------------
[Evaluator after step 360]: GOOD
Step 361
 chapter, chapter, chapter, chapter, chapter, final, chapter, chapter
chosen= chapter|entropy=0.022|T=0.6|K=500
----------------------------------------
Step 362
 in,.
, in, according, in,.
,.
,.

chosen=.
|entropy=1.188|T=0.6|K=500
----------------------------------------
Step 363
Chapter,**,**,[,This,(A,**,**
chosen=**|entropy=1.363|T=0.6|K=500
----------------------------------------
Step 364
Chapter,Chapter,Chapter,Chapter,Chapter,Just,Chapter,Chapter
chosen=Chapter|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 365
 , , , , , , , 
chosen= |entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 365]: GOOD
Step 366
2,2,2,2,2,2,2,2
chosen=2|entropy=0.008|T=0.6|K=500
----------------------------------------
Step 367
:,:,:,:,:,:,:,:
chosen=:|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 368
 Deep, Deep, Deep, Deep, Deep, Deep, Deep, The
chosen= Deep|entropy=0.146|T=0.6|K=500
----------------------------------------
Step 369
 Mathematics, Mathematics, Mathematics, Mathematics, Mathematics, Mathematics, Mathematics, Mathematics
chosen= Mathematics|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 370
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 370]: GOOD
Step 371
 Probability, Probability, Probability, Probability, Probability, Probability, Probability, Probability
chosen= Probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 372
 Theory, Theory, Theory, Theory, Theory, Theory, Theory, Theory
chosen= Theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 373
**

,**

,**

,**

,**

,**

,**

,**


chosen=**

|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 374
Probability,This,**,**,1,2,**,Probability
chosen=**|entropy=1.027|T=0.6|K=500
----------------------------------------
Step 375
2,2,2,2,2,Chapter,2,I
chosen=2|entropy=0.275|T=0.6|K=500
----------------------------------------
[Evaluator after step 375]: GOOD
Step 376
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 377
1,1,1,1,1,1,1,1
chosen=1|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 378
 Introduction, Introduction, Introduction, Introduction, Introduction, Introduction, Introduction, Introduction
chosen= Introduction|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 379
 to,**

, to, to, to,**
, to, to
chosen= to|entropy=0.069|T=0.6|K=500
----------------------------------------
Step 380
 Probability, Probability, Probability, Probability, Probability, Probability, Probability, Probability
chosen= Probability|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 380]: GOOD
Step 381
 Theory, Theory, Theory, Theory, Theory, Theory, Theory, Theory
chosen= Theory|entropy=0.023|T=0.6|K=500
----------------------------------------
Step 382
**

,**

,**

,**

,**

,**

,**

,**


chosen=**

|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 383
Probability,Probability,Probability,Probability,Probability,Probability,Probability,Probability
chosen=Probability|entropy=0.007|T=0.6|K=500
----------------------------------------
Step 384
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 385
 is, is, provides, is, is, provides, is, is
chosen= is|entropy=0.144|T=0.6|K=500
----------------------------------------
[Evaluator after step 385]: GOOD
Step 386
 a, a, a, a, an, a, a, a
chosen= a|entropy=0.063|T=0.6|K=500
----------------------------------------
Step 387
 mathematical, mathematical, fundamental, mathematical, cornerstone, fundamental, fundamental, mathematical
chosen= fundamental|entropy=1.175|T=0.6|K=500
----------------------------------------
Step 388
 mathematical, branch, concept, tool, branch, mathematical, branch, branch
chosen= branch|entropy=0.749|T=0.6|K=500
----------------------------------------
Step 389
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 390
 mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics
chosen= mathematics|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 390]: GOOD
Step 391
 that, that, used, that, that, that, that, that
chosen= that|entropy=0.043|T=0.6|K=500
----------------------------------------
Step 392
 provides, provides, deals, provides, govern, plays, deals, deals
chosen= deals|entropy=0.801|T=0.6|K=500
----------------------------------------
Step 393
 with, with, with, with, with, with, with, with
chosen= with|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 394
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.004|T=0.6|K=500
----------------------------------------
Step 395
 study, study, study, analysis, study, likelihood, study, study
chosen= study|entropy=0.688|T=0.6|K=500
----------------------------------------
[Evaluator after step 395]: GOOD
Step 396
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.008|T=0.6|K=500
----------------------------------------
Step 397
 random, random, random, random, chance, the, random, random
chosen= random|entropy=0.599|T=0.6|K=500
----------------------------------------
Step 398
 phenomena, events, events, phenomena, phenomena, events, phenomena, events
chosen= phenomena|entropy=0.523|T=0.6|K=500
----------------------------------------
Step 399
 and, and, and, and, and, and,., and
chosen=.|entropy=0.249|T=0.6|K=500
----------------------------------------
Step 400
 It, It, Unlike, It, It, One, It, It
chosen= It|entropy=0.095|T=0.6|K=500
----------------------------------------
[Evaluator after step 400]: GOOD
Step 401
 provides, provides, is, provides, provides, provides, provides, provides
chosen= provides|entropy=0.204|T=0.6|K=500
----------------------------------------
Step 402
 a, a, a, a, a, a, a, a
chosen= a|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 403
 framework, framework, systematic, framework, framework, framework, framework, framework
chosen= framework|entropy=0.242|T=0.6|K=500
----------------------------------------
Step 404
 for, for, for, for, for, for, for, for
chosen= for|entropy=0.034|T=0.6|K=500
----------------------------------------
Step 405
 modeling, analyzing, modeling, modeling, modeling, understanding, modeling, modeling
chosen= modeling|entropy=0.723|T=0.6|K=500
----------------------------------------
[Evaluator after step 405]: GOOD
Step 406
 and, and, and, uncertain, and, processes, and, and
chosen= and|entropy=0.754|T=0.6|K=500
----------------------------------------
Step 407
 analyzing, analyzing, analyzing, analyzing, analyzing, analyzing, analyzing, analyzing
chosen= analyzing|entropy=0.020|T=0.6|K=500
----------------------------------------
Step 408
 uncertain, situations, uncertain, systems, uncertain, situations, uncertain, uncertain
chosen= uncertain|entropy=0.901|T=0.6|K=500
----------------------------------------
Step 409
 or, events, events, events, outcomes, outcomes, outcomes, events
chosen= outcomes|entropy=0.861|T=0.6|K=500
----------------------------------------
Step 410
 and,,,,,,,,,,,,,,
chosen=,|entropy=0.932|T=0.6|K=500
----------------------------------------
[Evaluator after step 410]: GOOD
Step 411
 which, making, and, and, allowing, paving, making, and
chosen= making|entropy=1.343|T=0.6|K=500
----------------------------------------
Step 412
 it, it, it, it, it, it, it, it
chosen= it|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 413
 an, an, an, an, an, an, an, a
chosen= an|entropy=0.246|T=0.6|K=500
----------------------------------------
Step 414
 essential, essential, essential, invaluable, essential, essential, essential, essential
chosen= essential|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 415
 tool, tool, tool, tool, tool, tool, tool, tool
chosen= tool|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 415]: GOOD
Step 416
 for, for, for, in, for, for, for, in
chosen= for|entropy=0.693|T=0.7|K=200
----------------------------------------
Step 417
 understanding, understanding, various, scientific, understanding, both, various, various
chosen= various|entropy=0.918|T=0.6|K=500
----------------------------------------
Step 418
 scientific, applications, fields, fields, scientific, fields, scientific, scientific
chosen= scientific|entropy=1.054|T=0.6|K=500
----------------------------------------
Step 419
 and, and, and, disciplines, and,,, disciplines, investigations
chosen= disciplines|entropy=0.600|T=0.6|K=500
----------------------------------------
Step 420
.,., and,.,.,.,.,.
chosen=.|entropy=0.344|T=0.6|K=500
----------------------------------------
[Evaluator after step 420]: GOOD
Step 421
 At, The, Probability, The, At, Probability, Probability, Probability
chosen= Probability|entropy=0.959|T=0.6|K=500
----------------------------------------
Step 422
 theory, theory, theory, theory, theory, theory, theory, is
chosen= theory|entropy=0.015|T=0.6|K=500
----------------------------------------
Step 423
 is, is, is, finds, is, offers, is, is
chosen= is|entropy=0.109|T=0.6|K=500
----------------------------------------
Step 424
 built, built, concerned, built, based, based, built, built
chosen= built|entropy=0.896|T=0.6|K=500
----------------------------------------
Step 425
 upon, on, upon, upon, upon, upon, upon, upon
chosen= upon|entropy=0.455|T=0.6|K=500
----------------------------------------
[Evaluator after step 425]: GOOD
Step 426
 a, the, the, the, the, several, the, probability
chosen= the|entropy=1.132|T=0.6|K=500
----------------------------------------
Step 427
 principles, concept, principles, concept, mathematical, principles, concepts, concept
chosen= concepts|entropy=1.197|T=0.6|K=500
----------------------------------------
Step 428
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 429
 probability, probability, sets, chance, probability, also, probability, probability
chosen= probability|entropy=1.088|T=0.6|K=500
----------------------------------------
Step 430
,,,,,, itself, and, itself,,,,
chosen=,|entropy=0.398|T=0.6|K=500
----------------------------------------
[Evaluator after step 430]: GOOD
Step 431
 which, randomness, such, which, randomness, risk, probability, randomness
chosen= probability|entropy=1.261|T=0.6|K=500
----------------------------------------
Step 432
 distribution, distribution, distribution, distribution, distribution, spaces, distribution, distribution
chosen= distribution|entropy=0.754|T=0.6|K=500
----------------------------------------
Step 433
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 434
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 435
 random, stochastic, conditional, several, measure, probability, stochastic, sampling
chosen= stochastic|entropy=1.038|T=0.6|K=500
----------------------------------------
[Evaluator after step 435]: GOOD
Step 436
 processes, processes, behavior, processes, processes, processes, processes, processes
chosen= processes|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 437
,,,,.

,.

,.,,,.,.


chosen=.|entropy=0.770|T=0.6|K=500
----------------------------------------
Step 438
 It, The, Its, In, The, At, These, It
chosen= These|entropy=0.710|T=0.6|K=500
----------------------------------------
Step 439
 concepts, foundational, concepts, essential, mathematical, mathematical, mathematical, concepts
chosen= mathematical|entropy=0.555|T=0.6|K=500
----------------------------------------
Step 440
 structures, concepts, tools, structures, structures, concepts, structures, constructs
chosen= structures|entropy=1.330|T=0.6|K=500
----------------------------------------
[Evaluator after step 440]: GOOD
Step 441
 allow, allow, allow, allow, allow, allow, allow, allow
chosen= allow|entropy=0.167|T=0.6|K=500
----------------------------------------
Step 442
 us, us, us, us, us, researchers, us, us
chosen= us|entropy=0.255|T=0.6|K=500
----------------------------------------
Step 443
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 444
 quantify, quantify, assess, quantify, quantify, understand, quantify, quantify
chosen= quantify|entropy=0.318|T=0.6|K=500
----------------------------------------
Step 445
 the, and, the, the, uncertainty, the, the, uncertainty
chosen= the|entropy=0.935|T=0.6|K=500
----------------------------------------
[Evaluator after step 445]: GOOD
Step 446
 likelihood, likelihood, likelihood, likelihood, likelihood, unknown, likelihood, uncertainty
chosen= likelihood|entropy=0.037|T=0.6|K=500
----------------------------------------
Step 447
 of, of, of, of, of, that, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 448
 events, different, different, events, different, various, different, different
chosen= different|entropy=0.602|T=0.6|K=500
----------------------------------------
Step 449
 events, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, events
chosen= outcomes|entropy=0.490|T=0.6|K=500
----------------------------------------
Step 450
 and, in, in, and, and,,, and, and
chosen= and|entropy=1.020|T=0.6|K=500
----------------------------------------
[Evaluator after step 450]: GOOD
Step 451
 make, make, assess, analyze, understand, behaviors, assess, help
chosen= assess|entropy=1.310|T=0.6|K=500
----------------------------------------
Step 452
 the, the, the, the, the, how, the, the
chosen= the|entropy=0.074|T=0.6|K=500
----------------------------------------
Step 453
 behavior, behavior, relationships, reliability, relationships, relationships, probabilities, behavior
chosen= probabilities|entropy=1.887|T=0.6|K=500
----------------------------------------
Step 454
 associated, associated, associated, of, associated, associated, associated, associated
chosen= associated|entropy=0.246|T=0.6|K=500
----------------------------------------
Step 455
 with, with, with, with, with, with, with, with
chosen= with|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 455]: GOOD
Step 456
 various, uncertain, these, multiple, multiple, continuously, complex, various
chosen= complex|entropy=1.743|T=0.6|K=500
----------------------------------------
Step 457
 systems, systems, systems, systems, systems, systems, systems, systems
chosen= systems|entropy=0.187|T=0.6|K=500
----------------------------------------
Step 458
 involving,.

,.

,.

,.

,.

,.

,.


chosen=.

|entropy=0.121|T=0.6|K=500
----------------------------------------
Step 459
The,One,**,In,In,The,In,In
chosen=In|entropy=0.875|T=0.6|K=500
----------------------------------------
Step 460
 this, this, this, this, probability, providing, this, this
chosen= this|entropy=0.202|T=0.6|K=500
----------------------------------------
[Evaluator after step 460]: GOOD
Step 461
 chapter, chapter, chapter, chapter, chapter, chapter, chapter, chapter
chosen= chapter|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 462
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 463
 we, we, we, we, we, we, we, we
chosen= we|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 464
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 465
 explore, explore, explore, cover, begin, begin, explore, explore
chosen= explore|entropy=0.605|T=0.6|K=500
----------------------------------------
[Evaluator after step 465]: GOOD
Step 466
 the, the, the, the, the, several, the, the
chosen= the|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 467
 mathematical, fundamental, mathematical, mathematical, basic, intric, mathematical, mathematical
chosen= mathematical|entropy=0.998|T=0.6|K=500
----------------------------------------
Step 468
 foundations, structure, under, structure, foundation, formulations, foundations, structure
chosen= foundations|entropy=1.072|T=0.6|K=500
----------------------------------------
Step 469
 of, of, of, of, and, and, and, of
chosen= and|entropy=0.372|T=0.6|K=500
----------------------------------------
Step 470
 applications, applications, applications, applications, applications, principles, applications, applications
chosen= applications|entropy=0.065|T=0.6|K=500
----------------------------------------
[Evaluator after step 470]: GOOD
Step 471
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 472
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 473
 theory, theory, theory, theory, theory,,, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 474
.,.,.,.,., in,.,.
chosen=.|entropy=0.196|T=0.6|K=500
----------------------------------------
Step 475
 We, We, We, We, We, We, We, Initially
chosen= We|entropy=0.423|T=0.6|K=500
----------------------------------------
[Evaluator after step 475]: GOOD
Step 476
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 477
 start, begin, begin, study, start, start, begin, start
chosen= begin|entropy=0.824|T=0.6|K=500
----------------------------------------
Step 478
 by, by, by, by, by, by, by, by
chosen= by|entropy=0.152|T=0.6|K=500
----------------------------------------
Step 479
 defining, defining, defining, del, introducing, discussing, discussing, defining
chosen= discussing|entropy=0.757|T=0.6|K=500
----------------------------------------
Step 480
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.031|T=0.6|K=500
----------------------------------------
[Evaluator after step 480]: GOOD
Step 481
 basic, basic, basic, basic, basic, basic, basic, basic
chosen= basic|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 482
 definitions, definitions, definitions, concepts, definitions, concepts, concepts, concepts
chosen= concepts|entropy=0.713|T=0.6|K=500
----------------------------------------
Step 483
 of, of, of, that, and, such, of, of
chosen= of|entropy=0.306|T=0.6|K=500
----------------------------------------
Step 484
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 485
,,,,,, and,,, theory,,,,
chosen=,|entropy=0.193|T=0.6|K=500
----------------------------------------
[Evaluator after step 485]: GOOD
Step 486
 such, including, such, such, such, including, such, such
chosen= such|entropy=0.801|T=0.6|K=500
----------------------------------------
Step 487
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 488
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.158|T=0.6|K=500
----------------------------------------
Step 489
 probability, probability, probability, definition, probability, definition, probability, probability
chosen= probability|entropy=0.141|T=0.6|K=500
----------------------------------------
Step 490
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 490]: GOOD
Step 491
 an, an, an, an, an, an, an, an
chosen= an|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 492
 event, event, event, event, event, event, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 493
,,,,,,,,,,,,,,,
chosen=,|entropy=0.297|T=0.6|K=500
----------------------------------------
Step 494
 its, the, the, the, the, the, the, the
chosen= the|entropy=0.208|T=0.6|K=500
----------------------------------------
Step 495
 probability, probability, probability, probability, concept, probability, probability, probability
chosen= probability|entropy=0.004|T=0.6|K=500
----------------------------------------
[Evaluator after step 495]: GOOD
Step 496
 distribution, distribution, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 497
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 498
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 499
 the, the, the, the, the, how, the, the
chosen= the|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 500
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.003|T=0.6|K=500
----------------------------------------
[Evaluator after step 500]: GOOD
Step 501
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 502
 multiple, multiple, multiple, multiple, multiple, multiple, multiple, multiple
chosen= multiple|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 503
 events, events, events, events, events, events, events, events
chosen= events|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 504
.,.,.,.,.,.,.,.
chosen=.|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 505
 We, We, Then, We, We, Furthermore, We, We
chosen= We|entropy=0.136|T=0.6|K=500
----------------------------------------
[Evaluator after step 505]: GOOD
Step 506
 will, will, will, will, will, will, will, will
chosen= will|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 507
 then, then, also, also, then, also, also, then
chosen= also|entropy=0.694|T=0.6|K=500
----------------------------------------
Step 508
 delve, delve, delve, examine, delve, discuss, delve, delve
chosen= delve|entropy=0.217|T=0.6|K=500
----------------------------------------
Step 509
 into, into, into, into, into, into, into, deeper
chosen= into|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 510
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 510]: GOOD
Step 511
 mathematical, mathematical, mathematical, mathematical, mathematical, mathematical, mathematical, mathematical
chosen= mathematical|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 512
 foundations, foundations, foundations, foundations, foundations, foundations, foundations, foundation
chosen= foundations|entropy=0.413|T=0.6|K=500
----------------------------------------
Step 513
 of, of, of, of, of,,, of, of
chosen= of|entropy=0.140|T=0.6|K=500
----------------------------------------
Step 514
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 515
,,,,,,,,,,,,,,,
chosen=,|entropy=0.072|T=0.6|K=500
----------------------------------------
[Evaluator after step 515]: GOOD
Step 516
 including, including, including, including, including, including, including, including
chosen= including|entropy=0.004|T=0.6|K=500
----------------------------------------
Step 517
 concepts, concepts, concepts, concepts, measure, concepts, concepts, measure
chosen= concepts|entropy=0.507|T=0.6|K=500
----------------------------------------
Step 518
 such, such, such, such, such, such, such, of
chosen= such|entropy=0.070|T=0.6|K=500
----------------------------------------
Step 519
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 520
 measure, measure, measure, measure, measure,...

, measure, measure
chosen= measure|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 520]: GOOD
Step 521
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 522
,,,,,,,,,,,,,,,
chosen=,|entropy=0.012|T=0.6|K=500
----------------------------------------
Step 523
 stochastic, stochastic, stochastic, stochastic, stochastic, stochastic, stochastic, stochastic
chosen= stochastic|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 524
 processes, processes, processes, processes, processes, processes, processes, processes
chosen= processes|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 525
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 525]: GOOD
Step 526
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 527
 conditional, conditional, conditional, conditional, conditional, conditional, conditional, conditional
chosen= conditional|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 528
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 529
.

,.,.

,.

,.

,.,.

,.


chosen=.

|entropy=0.426|T=0.6|K=500
----------------------------------------
Step 530
**,The,**,(prob,**,**,**,It
chosen=**|entropy=0.794|T=0.6|K=500
----------------------------------------
[Evaluator after step 530]: GOOD
Step 531
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 532
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.8|K=400
----------------------------------------
Step 533
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 534
 Probability, Probability, The, Basic, Probability, Fundamental, Probability, Basic
chosen= Probability|entropy=0.682|T=0.6|K=500
----------------------------------------
Step 535
 Concepts, and, Theory, Fund, Concepts, Distribution, Concepts, and
chosen= Concepts|entropy=0.927|T=0.6|K=500
----------------------------------------
[Evaluator after step 535]: GOOD
Step 536
**

,**

,**

,**

, and,**

,**

,**


chosen=**

|entropy=0.128|T=0.6|K=500
----------------------------------------
Step 537
2,2,In,2,2, **,**,**
chosen=**|entropy=0.575|T=0.6|K=500
----------------------------------------
Step 538
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 539
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 540
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 540]: GOOD
Step 541
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 542
1,1,1,1,1,1,1,1
chosen=1|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 543
 Definition, Basic, The, Basic, Basic, The, Probability, Probability
chosen= Probability|entropy=0.441|T=0.6|K=500
----------------------------------------
Step 544
 of, of,**

,**

, of,:, of, of
chosen= of|entropy=0.719|T=0.6|K=500
----------------------------------------
Step 545
 an, an, an, an, an, an, an, an
chosen= an|entropy=0.018|T=0.6|K=500
----------------------------------------
[Evaluator after step 545]: GOOD
Step 546
 Event, Event, Event, Event, Event, Event, Event, Event
chosen= Event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 547
**

,**

,**

,**

,**

,**

,**

,**


chosen=**

|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 548
In,The,In,Probability,The,The,In,In
chosen=In|entropy=0.891|T=0.6|K=500
----------------------------------------
Step 549
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 550
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.038|T=0.6|K=500
----------------------------------------
[Evaluator after step 550]: GOOD
Step 551
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 552
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.056|T=0.6|K=500
----------------------------------------
Step 553
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.016|T=0.6|K=500
----------------------------------------
Step 554
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 555
 an, an, an, an, an, an, an, an
chosen= an|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 555]: GOOD
Step 556
 event, event, event, event, event, event, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 557
 is, is, occurring, is, is, is, is, can
chosen= is|entropy=0.095|T=0.6|K=500
----------------------------------------
Step 558
 a, defined, a, defined, a, a, defined, the
chosen= defined|entropy=0.748|T=0.6|K=500
----------------------------------------
Step 559
 as, as, as, as, as, by, as, as
chosen= as|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 560
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.011|T=0.6|K=500
----------------------------------------
[Evaluator after step 560]: GOOD
Step 561
 ratio, measure, measure, measure, proportion, marginal, ratio, ratio
chosen= ratio|entropy=1.143|T=0.6|K=500
----------------------------------------
Step 562
 of, of, of, between, of, of, of, of
chosen= of|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 563
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 564
 number, number, number, number, number, number, number, number
chosen= number|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 565
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 565]: GOOD
Step 566
 favorable, favorable, favorable, favorable, favorable, favorable, favorable, favorable
chosen= favorable|entropy=0.007|T=0.6|K=500
----------------------------------------
Step 567
 outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes
chosen= outcomes|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 568
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 569
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 570
 total, total, total, total, total, total, total, total
chosen= total|entropy=0.004|T=0.6|K=500
----------------------------------------
[Evaluator after step 570]: GOOD
Step 571
 number, number, number, number, number, number, number, number
chosen= number|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 572
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 573
 possible, possible, possible, possible, possible, possible, possible, possible
chosen= possible|entropy=0.012|T=0.6|K=500
----------------------------------------
Step 574
 outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes
chosen= outcomes|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 575
.,.,.,.,.,.,.,.
chosen=.|entropy=0.156|T=0.6|K=500
----------------------------------------
[Evaluator after step 575]: GOOD
Step 576
 For, This, The, This, This, For, Math, For
chosen= Math|entropy=0.714|T=0.6|K=500
----------------------------------------
Step 577
em,em,em,em,em,em,em,em
chosen=em|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 578
atically,atically,atically,atically,atically,atically,atically,atically
chosen=atically|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 579
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 580
 this, this, if, this, this, this, this, this
chosen= this|entropy=0.078|T=0.6|K=500
----------------------------------------
[Evaluator after step 580]: GOOD
Step 581
 can, can, can, is, is, is, can, can
chosen= can|entropy=0.655|T=0.6|K=500
----------------------------------------
Step 582
 be, be, be, be, be, be, be, be
chosen= be|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 583
 expressed, expressed, expressed, expressed, expressed, expressed, expressed, represented
chosen= expressed|entropy=0.240|T=0.6|K=500
----------------------------------------
Step 584
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 585
:

,:

,:

,:
,:

,:

,:

,:


chosen=:

|entropy=0.035|T=0.6|K=500
----------------------------------------
[Evaluator after step 585]: GOOD
Step 586
$$,$,P,P,$$,P,$$,P
chosen=$$|entropy=0.542|T=0.6|K=500
----------------------------------------
Step 587

,
,
,
,
, p,
,

chosen=
|entropy=0.547|T=0.6|K=500
----------------------------------------
Step 588
P,P,P,P,P,P,P,P
chosen=P|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 589
(E,(A,(A,(A,(A,(S,(A,(A
chosen=(A|entropy=0.314|T=0.6|K=500
----------------------------------------
Step 590
),),),|,),),),)
chosen=)|entropy=0.007|T=0.6|K=500
----------------------------------------
[Evaluator after step 590]: GOOD
Step 591
 =, =, =, =, =, =, =, =
chosen= =|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 592
 \, \, \, \, \, \, \, \
chosen= \|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 593
frac,frac,frac,frac,frac,frac,frac,frac
chosen=frac|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 594
{\,{,{\,{\,{\,{,{\,{
chosen={\|entropy=0.694|T=0.6|K=500
----------------------------------------
Step 595
text,text,text,text,text,text,text,text
chosen=text|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 595]: GOOD
Step 596
{,{,{,{,{,{,{,{
chosen={|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 597
Number,Number,Number,Number,Number,Number,Number,Number
chosen=Number|entropy=0.096|T=0.6|K=500
----------------------------------------
Step 598
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 599
 favorable, favorable, favorable, favorable, Favor, favorable, favorable, favorable
chosen= favorable|entropy=0.338|T=0.6|K=500
----------------------------------------
Step 600
 outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes
chosen= outcomes|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 600]: GOOD
Step 601
}},}},}},}},}},}},}},}}
chosen=}}|entropy=0.152|T=0.6|K=500
----------------------------------------
Step 602
{\,{\,{\,{\,{\,{\,{\,{\
chosen={\|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 603
text,text,text,text,text,text,text,text
chosen=text|entropy=0.001|T=0.8|K=400
----------------------------------------
Step 604
{,{,{,{,{,{,{,{
chosen={|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 605
Total,Total,Total,Total,Total,Total,Total,Total
chosen=Total|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 605]: GOOD
Step 606
 number, number, number, number, number, number, number, number
chosen= number|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 607
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 608
 possible, possible, possible, possible, possible, possible, possible, possible
chosen= possible|entropy=0.030|T=0.6|K=500
----------------------------------------
Step 609
 outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes, outcomes
chosen= outcomes|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 610
}}
,}}
,}}
,}}
,}}
,}}
,}}
,}}

chosen=}}
|entropy=0.008|T=0.6|K=500
----------------------------------------
[Evaluator after step 610]: GOOD
Step 611
$$,$$,$$,$$,$$,$$,$$,$$
chosen=$$|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 612


,

,

,

,

,

,

,


chosen=

|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 613
This,This,This,For,This,where,This,This
chosen=This|entropy=0.634|T=0.6|K=500
----------------------------------------
Step 614
 concept, concept, definition, definition, concept, property, concept, concept
chosen= concept|entropy=0.379|T=0.6|K=500
----------------------------------------
Step 615
 is, is, under, is, is, of, is, helps
chosen= is|entropy=0.284|T=0.6|K=500
----------------------------------------
[Evaluator after step 615]: GOOD
Step 616
 fundamental, fundamental, fundamental, fundamental, pivotal, fundamental, fundamental, fundamental
chosen= fundamental|entropy=0.626|T=0.6|K=500
----------------------------------------
Step 617
 in, to, in, to, in, to, in, in
chosen= in|entropy=0.566|T=0.6|K=500
----------------------------------------
Step 618
 probability, understanding, understanding, probability, understanding, probability, understanding, probability
chosen= understanding|entropy=0.495|T=0.6|K=500
----------------------------------------
Step 619
 the, how, the, the, the, probabilities, how, how
chosen= how|entropy=0.438|T=0.6|K=500
----------------------------------------
Step 620
 probabilities, probabilities, probabilities, events, events, events, events, we
chosen= events|entropy=1.489|T=0.6|K=500
----------------------------------------
[Evaluator after step 620]: GOOD
Step 621
 can, can, occur, can, are, typically, can, can
chosen= can|entropy=0.539|T=0.6|K=500
----------------------------------------
Step 622
 occur, occur, occur, occur, occur, correspond, occur, be
chosen= occur|entropy=0.321|T=0.6|K=500
----------------------------------------
Step 623
 and, and, and, under, and, and, and, in
chosen= and|entropy=0.291|T=0.6|K=500
----------------------------------------
Step 624
 how, calculate, what, how, how, the, predict, how
chosen= predict|entropy=0.774|T=0.6|K=500
----------------------------------------
Step 625
 their, their, their, their, their, their, their, their
chosen= their|entropy=0.174|T=0.6|K=500
----------------------------------------
[Evaluator after step 625]: GOOD
Step 626
 likelihood, probabilities, likelihood, chances, likelihood, likelihood, likelihood, likelihood
chosen= likelihood|entropy=0.503|T=0.6|K=500
----------------------------------------
Step 627
s,.,.,.,.

,.,s,s
chosen=s|entropy=0.957|T=0.6|K=500
----------------------------------------
Step 628
.,.,.

,.

,., under,.,.
chosen=.|entropy=0.645|T=0.6|K=500
----------------------------------------
Step 629
 The, For, Probability, The, Probability, The, The, For
chosen= The|entropy=1.247|T=0.6|K=500
----------------------------------------
Step 630
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.008|T=0.6|K=500
----------------------------------------
[Evaluator after step 630]: GOOD
Step 631
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.097|T=0.6|K=500
----------------------------------------
Step 632
 an, an, an, an, an, an, an, an
chosen= an|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 633
 event, event, event, event, event, even, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 634
 is, can, is, being, is, can, is, is
chosen= is|entropy=0.697|T=0.6|K=500
----------------------------------------
Step 635
 a, typically, a, a, always, usually, a, typically
chosen= a|entropy=0.537|T=0.6|K=500
----------------------------------------
[Evaluator after step 635]: GOOD
Step 636
 measure, measure, measure, value, measure, measure, measure, measure
chosen= measure|entropy=0.334|T=0.6|K=500
----------------------------------------
Step 637
 of, of, that, that, of, of, of, of
chosen= of|entropy=0.159|T=0.6|K=500
----------------------------------------
Step 638
 how, its, how, uncertainty, uncertainty, uncertainty, how, the
chosen= how|entropy=1.176|T=0.6|K=500
----------------------------------------
Step 639
 likely, likely, likely, likely, likely, likely, likely, likely
chosen= likely|entropy=0.116|T=0.6|K=500
----------------------------------------
Step 640
 it, it, it, it, it, it, it, it
chosen= it|entropy=0.032|T=0.6|K=500
----------------------------------------
[Evaluator after step 640]: GOOD
Step 641
 is, is, is, is, is, is, is, is
chosen= is|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 642
 to, that, to, that, to, to, to, to
chosen= to|entropy=0.639|T=0.6|K=500
----------------------------------------
Step 643
 occur, occur, occur, occur, occur, occur, occur, occur
chosen= occur|entropy=0.187|T=0.6|K=500
----------------------------------------
Step 644
,, within,,, under,,,,,,,,
chosen=,|entropy=0.754|T=0.6|K=500
----------------------------------------
Step 645
 with, ranging, with, with, with, ranging, ranging, with
chosen= ranging|entropy=1.191|T=0.6|K=500
----------------------------------------
[Evaluator after step 645]: GOOD
Step 646
 from, from, from, from, from, from, from, from
chosen= from|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 647
 , , , , , , , 
chosen= |entropy=0.001|T=0.6|K=500
----------------------------------------
Step 648
0,0,0,0,0,0,0,0
chosen=0|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 649
 (, (, to, (, (, (, (, (
chosen= (|entropy=0.475|T=0.6|K=500
----------------------------------------
Step 650
im,im,im,in,im,probability,im,im
chosen=im|entropy=0.115|T=0.6|K=500
----------------------------------------
[Evaluator after step 650]: GOOD
Step 651
possible,possible,possible,possible,possible,possible,possible,possible
chosen=possible|entropy=0.151|T=0.6|K=500
----------------------------------------
Step 652
),),),), event, event,),)
chosen=)|entropy=0.368|T=0.6|K=500
----------------------------------------
Step 653
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 654
 , , , , , , , 
chosen= |entropy=0.001|T=0.7|K=200
----------------------------------------
Step 655
1,1,1,1,1,1,1,1
chosen=1|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 655]: GOOD
Step 656
 (, (, (, (, (, (, (, (
chosen= (|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 657
sure,cert,c,c,sure,cert,cert,c
chosen=cert|entropy=0.791|T=0.6|K=500
----------------------------------------
Step 658
ainty,ainty,ainty,ainty,ainty,ainty,ainty,ainty
chosen=ainty|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 659
).

,).,).

,).

,).

,).

,).

,).


chosen=).

|entropy=0.023|T=0.6|K=500
----------------------------------------
Step 660
**,**,**,**,**,**,**,**
chosen=**|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 660]: GOOD
Step 661
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 662
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.9|K=1000
----------------------------------------
Step 663
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 664
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 665
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 665]: GOOD
Step 666
 Probability, Probability, Probability, Probability, Probability, Probability, Probability, Probability
chosen= Probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 667
 Distribution, Distribution, Distribution, Distribution, Distribution, Distribution, Distribution, Distribution
chosen= Distribution|entropy=0.038|T=0.6|K=500
----------------------------------------
Step 668
**

,**

,**

,**

,**

,**

,**

,**


chosen=**

|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 669
A,A,A,A,A,In,A,A
chosen=A|entropy=0.067|T=0.6|K=500
----------------------------------------
Step 670
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 670]: GOOD
Step 671
 distribution, distribution, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 672
 is, is, describes, describes, is, describes, is, describes
chosen= is|entropy=0.818|T=0.6|K=500
----------------------------------------
Step 673
 a, a, a, a, a, a, a, a
chosen= a|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 674
 function, function, function, function, function, function, function, function
chosen= function|entropy=0.177|T=0.6|K=500
----------------------------------------
Step 675
 that, that, that, that, that, that, that, that
chosen= that|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 675]: GOOD
Step 676
 describes, describes, describes, describes, describes, shows, assigns, assigns
chosen= assigns|entropy=0.781|T=0.6|K=500
----------------------------------------
Step 677
 probabilities, probabilities, probabilities, to, probabilities, probabilities, probabilities, probabilities
chosen= probabilities|entropy=0.282|T=0.6|K=500
----------------------------------------
Step 678
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 679
 each, all, each, all, all, Each, each, each
chosen= each|entropy=0.919|T=0.6|K=500
----------------------------------------
Step 680
 possible, possible, possible, possible, possible, possible, possible, possible
chosen= possible|entropy=0.159|T=0.6|K=500
----------------------------------------
[Evaluator after step 680]: GOOD
Step 681
 outcome, outcome, outcome, outcome, outcome, outcome, outcome, outcome
chosen= outcome|entropy=0.016|T=0.6|K=500
----------------------------------------
Step 682
 of, in, of, of, of, in, in, of
chosen= in|entropy=0.330|T=0.6|K=500
----------------------------------------
Step 683
 a, a, an, an, a, a, a, a
chosen= a|entropy=0.064|T=0.6|K=500
----------------------------------------
Step 684
 random, given, random, population, set, given, random, given
chosen= random|entropy=0.845|T=0.6|K=500
----------------------------------------
Step 685
 variable, variable, experiment, variable, variable, variable, experiment, variable
chosen= experiment|entropy=0.324|T=0.6|K=500
----------------------------------------
[Evaluator after step 685]: GOOD
Step 686
.,.,.,.,., with,.,.
chosen=.|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 687
 This, This, It, It, In, This, This, It
chosen= This|entropy=0.758|T=0.6|K=500
----------------------------------------
Step 688
 function, distribution, distribution, allows, distribution, function, function, distribution
chosen= function|entropy=0.690|T=0.6|K=500
----------------------------------------
Step 689
 is, shows, shows, is, provides, is, can, is
chosen= can|entropy=1.195|T=0.6|K=500
----------------------------------------
Step 690
 be, be, be, be, be, take, be, take
chosen= be|entropy=0.298|T=0.6|K=500
----------------------------------------
[Evaluator after step 690]: GOOD
Step 691
 continuous, un, either, a, discrete, continuous, continuous, either
chosen= continuous|entropy=1.034|T=0.6|K=500
----------------------------------------
Step 692
 or, or, or, or, or, (, or, or
chosen= or|entropy=0.045|T=0.6|K=500
----------------------------------------
Step 693
 discrete, discrete, discrete, discrete, discrete, discrete, discrete, discrete
chosen= discrete|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 694
 and,,, and, and,,, and,,, and
chosen=,|entropy=0.724|T=0.6|K=500
----------------------------------------
Step 695
 depending, and, depending, depending, depending, depending, depending, depending
chosen= depending|entropy=0.171|T=0.6|K=500
----------------------------------------
[Evaluator after step 695]: GOOD
Step 696
 on, on, on, on, on, on, on, on
chosen= on|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 697
 the, whether, the, the, the, the, the, the
chosen= the|entropy=0.046|T=0.6|K=500
----------------------------------------
Step 698
 nature, nature, nature, nature, nature, nature, nature, nature
chosen= nature|entropy=0.046|T=0.6|K=500
----------------------------------------
Step 699
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 700
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 700]: GOOD
Step 701
 experiment, experiment, random, experiment, experiment, experiment, experiment, experiment
chosen= experiment|entropy=0.674|T=0.6|K=500
----------------------------------------
Step 702
.,.,.,.,.,.,.,.
chosen=.|entropy=0.021|T=0.6|K=500
----------------------------------------
Step 703
 It, For, The, For, It, For, For, For
chosen= For|entropy=0.586|T=0.6|K=500
----------------------------------------
Step 704
 example, example, a, a, example, example, example, example
chosen= example|entropy=0.218|T=0.6|K=500
----------------------------------------
Step 705
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 705]: GOOD
Step 706
 a, a, the, a, the, a, a, in
chosen= a|entropy=1.045|T=0.6|K=500
----------------------------------------
Step 707
 discrete, discrete, discrete, random, probability, probability, continuous, bin
chosen= continuous|entropy=1.600|T=0.6|K=500
----------------------------------------
Step 708
 probability, probability, random, probability, distribution, probability, probability, probability
chosen= probability|entropy=0.823|T=0.6|K=500
----------------------------------------
Step 709
 distribution, distribution, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 710
 might, assigns, assigns, models, for, formulas, assigns, like
chosen= assigns|entropy=1.312|T=0.6|K=500
----------------------------------------
[Evaluator after step 710]: GOOD
Step 711
 probabilities, probabilities, probabilities, probabilities, probabilities, probabilities, probabilities, probabilities
chosen= probabilities|entropy=0.050|T=0.6|K=500
----------------------------------------
Step 712
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 713
 real, intervals, a, continuously, a, events, a, a
chosen= a|entropy=1.130|T=0.6|K=500
----------------------------------------
Step 714
 continuous, range, range, continuous, continuous, range, range, continuous
chosen= range|entropy=0.750|T=0.6|K=500
----------------------------------------
Step 715
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 715]: GOOD
Step 716
 values, values, values, outcomes, values, values, values, values
chosen= values|entropy=0.751|T=0.6|K=500
----------------------------------------
Step 717
,,,,,,,,,,,,,,,
chosen=,|entropy=0.032|T=0.6|K=500
----------------------------------------
Step 718
 while, while, whereas, whereas, whereas, while, while, while
chosen= while|entropy=0.056|T=0.6|K=500
----------------------------------------
Step 719
 a, a, a, a, a, a, a, a
chosen= a|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 720
 discrete, discrete, discrete, discrete, discrete, discreet, discrete, discrete
chosen= discrete|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 720]: GOOD
Step 721
 distribution, probability, distribution, distribution, distribution, probability, probability, probability
chosen= probability|entropy=0.685|T=0.6|K=500
----------------------------------------
Step 722
 distribution, distribution, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 723
 assigns, assigns, assigns, assigns, assigns, assigns, assigns, assigns
chosen= assigns|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 724
 probabilities, probabilities, probabilities, probabilities, probabilities, probabilities, probabilities, probabilities
chosen= probabilities|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 725
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 725]: GOOD
Step 726
 a, specific, a, specific, specific, distinct, a, a
chosen= a|entropy=0.875|T=0.6|K=500
----------------------------------------
Step 727
 finite, finite, finite, finite, finite, finite, finite, finite
chosen= finite|entropy=0.179|T=0.6|K=500
----------------------------------------
Step 728
 set, set, number, set, set, set, set, set
chosen= set|entropy=0.097|T=0.6|K=500
----------------------------------------
Step 729
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 730
 values, outcomes, values, values, values, outcomes, values, outcomes
chosen= values|entropy=0.454|T=0.6|K=500
----------------------------------------
[Evaluator after step 730]: GOOD
Step 731
.

,.

,.

,.

,.

,.

,.

,.


chosen=.

|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 732
The,It,Probability,Frequency,A,**,The,Probability
chosen=The|entropy=1.249|T=0.6|K=500
----------------------------------------
Step 733
 probability, cumulative, probability, probability, probability, stationary, concept, most
chosen= concept|entropy=0.231|T=0.6|K=500
----------------------------------------
Step 734
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 735
 probability, probability, probability, a, probability, a, probability, probability
chosen= probability|entropy=0.427|T=0.6|K=500
----------------------------------------
[Evaluator after step 735]: GOOD
Step 736
 distribution, distributions, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.026|T=0.6|K=500
----------------------------------------
Step 737
 is, is, is, is, is, broad, is, is
chosen= is|entropy=0.124|T=0.6|K=500
----------------------------------------
Step 738
 crucial, crucial, essential, crucial, essential, crucial, crucial, crucial
chosen= crucial|entropy=0.367|T=0.6|K=500
----------------------------------------
Step 739
 in, in, in, in, in, for, in, in
chosen= in|entropy=0.155|T=0.6|K=500
----------------------------------------
Step 740
 understanding, understanding, understanding, various, statistical, understanding, understanding, quantitative
chosen= understanding|entropy=0.329|T=0.6|K=500
----------------------------------------
[Evaluator after step 740]: GOOD
Step 741
 the, the, the, the, the, how, the, the
chosen= the|entropy=0.476|T=0.6|K=500
----------------------------------------
Step 742
 behavior, likelihood, behavior, likelihood, behavior, long, behavior, behavior
chosen= behavior|entropy=0.182|T=0.6|K=500
----------------------------------------
Step 743
 of, of, of, of, of, of, of, and
chosen= of|entropy=0.115|T=0.6|K=500
----------------------------------------
Step 744
 random, random, random, random, a, random, random, stochastic
chosen= random|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 745
 variables, variables, variables, variables, variables, variables, variables, variables
chosen= variables|entropy=0.026|T=0.6|K=500
----------------------------------------
[Evaluator after step 745]: GOOD
Step 746
.,., and, and,.,., and, and
chosen= and|entropy=0.530|T=0.6|K=500
----------------------------------------
Step 747
 how, their, deriving, examining, their, how, how, how
chosen= how|entropy=0.784|T=0.6|K=500
----------------------------------------
Step 748
 they, they, they, they, they, they, they, they
chosen= they|entropy=0.020|T=0.6|K=500
----------------------------------------
Step 749
 relate, are, relate, relate, can, can, relate, are
chosen= relate|entropy=0.617|T=0.6|K=500
----------------------------------------
Step 750
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 750]: GOOD
Step 751
 each, their, each, individual, each, experimental, each, other
chosen= each|entropy=0.875|T=0.6|K=500
----------------------------------------
Step 752
 other, other, other, other, other, other, other, other
chosen= other|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 753
.,.,.,.,.,.,.,.
chosen=.|entropy=0.029|T=0.6|K=500
----------------------------------------
Step 754
 It, It, It, By, It, A, A, By
chosen= A|entropy=0.208|T=0.6|K=500
----------------------------------------
Step 755
 random, random, distribution, probability, random, random, random, probability
chosen= random|entropy=0.916|T=0.6|K=500
----------------------------------------
[Evaluator after step 755]: GOOD
Step 756
 variable, variable, variable, variable, variable, variable, variable, variable
chosen= variable|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 757
 X, can, can, represented, is, can, can, is
chosen= can|entropy=0.669|T=0.6|K=500
----------------------------------------
Step 758
 have, take, be, have, have, be, have, have
chosen= have|entropy=1.062|T=0.6|K=500
----------------------------------------
Step 759
 various, a, different, different, various, to, a, a
chosen= a|entropy=0.770|T=0.6|K=500
----------------------------------------
Step 760
 probability, probability, discrete, specific, discrete, range, probability, different
chosen= probability|entropy=0.428|T=0.6|K=500
----------------------------------------
[Evaluator after step 760]: GOOD
Step 761
 distribution, distribution, distribution, distribution, distribution, distribution, distribution, distribution
chosen= distribution|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 762
,, that, that, that, that, that, that, that
chosen= that|entropy=0.278|T=0.6|K=500
----------------------------------------
Step 763
 describes, is, reflects, represents, is, either, is, models
chosen= is|entropy=1.158|T=0.6|K=500
----------------------------------------
Step 764
 continuous, continuous, continuous, used, continuous, interpre, continuous, either
chosen= continuous|entropy=0.423|T=0.6|K=500
----------------------------------------
Step 765
 or, or,,, or, or, but, or, or
chosen= or|entropy=0.153|T=0.6|K=500
----------------------------------------
[Evaluator after step 765]: GOOD
Step 766
 discrete, discrete, discrete, discrete, discrete, discrete, discrete, discrete
chosen= discrete|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 767
,,,,,,.

,,,.

,,,.


chosen=,|entropy=0.024|T=0.6|K=500
----------------------------------------
Step 768
 and, and, and, and, and, second, and, which
chosen= and|entropy=0.202|T=0.6|K=500
----------------------------------------
Step 769
 it, the, it, the, this, this, the, these
chosen= the|entropy=1.443|T=0.6|K=500
----------------------------------------
Step 770
 distribution, shape, distribution, distribution, distribution, properties, properties, properties
chosen= properties|entropy=0.831|T=0.6|K=500
----------------------------------------
[Evaluator after step 770]: GOOD
Step 771
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.041|T=0.6|K=500
----------------------------------------
Step 772
 these, these, these, these, the, the, these, these
chosen= these|entropy=1.014|T=0.6|K=500
----------------------------------------
Step 773
 distributions, distributions, distributions, distributions, distributions, distributions, distributions, distributions
chosen= distributions|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 774
 are, can, are,—are, are, are, can, can
chosen= can|entropy=1.045|T=0.6|K=500
----------------------------------------
Step 775
 be, be, be, be, be, help, be, be
chosen= be|entropy=0.383|T=0.6|K=500
----------------------------------------
[Evaluator after step 775]: GOOD
Step 776
 used, used, explored, used, used, calculated, used, analyzed
chosen= used|entropy=0.417|T=0.6|K=500
----------------------------------------
Step 777
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.008|T=0.6|K=500
----------------------------------------
Step 778
 describe, model, analyze, model, make, analyze, describe, model
chosen= describe|entropy=1.656|T=0.6|K=500
----------------------------------------
Step 779
 the, and, and, and, the, measurements, and, and
chosen= and|entropy=0.709|T=0.6|K=500
----------------------------------------
Step 780
 analyze, analyze, analyze, analyze, predict, analyze, analyze, analyze
chosen= analyze|entropy=0.123|T=0.6|K=500
----------------------------------------
[Evaluator after step 780]: GOOD
Step 781
 the, random, the, the, the, random, the, random
chosen= the|entropy=0.753|T=0.6|K=500
----------------------------------------
Step 782
 behavior, behavior, behavior, outcomes, outcomes, outcomes, behavior, behavior
chosen= behavior|entropy=0.513|T=0.6|K=500
----------------------------------------
Step 783
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 784
 the, the, the, the, the, the, random, random
chosen= random|entropy=0.624|T=0.6|K=500
----------------------------------------
Step 785
 processes, variables, events, processes, events, processes, processes, systems
chosen= processes|entropy=1.031|T=0.6|K=500
----------------------------------------
[Evaluator after step 785]: GOOD
Step 786
.

,.

,.

,.

,.

,.

,.

,.


chosen=.

|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 787
**,**,**,**,**,**,**,**
chosen=**|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 788
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 789
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.9|K=1000
----------------------------------------
Step 790
2,2,2,2,2,2,2,2
chosen=2|entropy=0.007|T=0.6|K=500
----------------------------------------
[Evaluator after step 790]: GOOD
Step 791
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 792
3,3,3,3,3,3,3,3
chosen=3|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 793
 Probability, Probability, Probability, Conditional, Probability, Conditional, Probability, Probability
chosen= Probability|entropy=0.686|T=0.6|K=500
----------------------------------------
Step 794
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 795
 Multiple, Multiple, Multiple, Multiple, Multiple, Multiple, Multiple, Multiple
chosen= Multiple|entropy=0.003|T=0.6|K=500
----------------------------------------
[Evaluator after step 795]: GOOD
Step 796
 Events, Events, Events, Events, Events, Events, Events, Events
chosen= Events|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 797
**

,**

,**

,**

,**

,**

,**

,**


chosen=**

|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 798
When,When,When,The,Probability,When,When,When
chosen=When|entropy=0.743|T=0.6|K=500
----------------------------------------
Step 799
 dealing, dealing, considering, dealing, dealing, evaluating, dealing, dealing
chosen= dealing|entropy=0.294|T=0.6|K=500
----------------------------------------
Step 800
 with, with, with, with, with, with, with, with
chosen= with|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 800]: GOOD
Step 801
 multiple, multiple, multiple, multiple, multiple, the, multiple, multiple
chosen= multiple|entropy=0.043|T=0.6|K=500
----------------------------------------
Step 802
 events, events, events, events, events, events, events, events
chosen= events|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 803
,,,,,,,,,, in,,,,
chosen=,|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 804
 the, the, the, it, the, it, it, we
chosen= it|entropy=0.774|T=0.6|K=500
----------------------------------------
Step 805
 is, is, is, is, is, is, is,'s
chosen= is|entropy=0.033|T=0.6|K=500
----------------------------------------
[Evaluator after step 805]: GOOD
Step 806
 important, common, important, important, important, often, important, important
chosen= important|entropy=0.589|T=0.6|K=500
----------------------------------------
Step 807
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 808
 understand, consider, consider, understand, understand, consider, consider, consider
chosen= consider|entropy=0.455|T=0.6|K=500
----------------------------------------
Step 809
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.268|T=0.6|K=500
----------------------------------------
Step 810
 probabilities, probabilities, probability, interactions, probability, interaction, probabilities, relationship
chosen= probabilities|entropy=1.346|T=0.6|K=500
----------------------------------------
[Evaluator after step 810]: GOOD
Step 811
 of, of, of, associated, of, of, of, of
chosen= of|entropy=0.269|T=0.6|K=500
----------------------------------------
Step 812
 each, each, each, each, these, their, each, their
chosen= each|entropy=0.798|T=0.6|K=500
----------------------------------------
Step 813
 event, event, event, event, event, event, event, event
chosen= event|entropy=0.143|T=0.6|K=500
----------------------------------------
Step 814
 and, occurring, occurring, independently, and, separately, occurring, occurring
chosen= occurring|entropy=1.100|T=0.6|K=500
----------------------------------------
Step 815
 independently, separately, independently, independently, independently, and, independently, independently
chosen= independently|entropy=0.285|T=0.6|K=500
----------------------------------------
[Evaluator after step 815]: GOOD
Step 816
 and,.,.,,, of, of, and,.
chosen= and|entropy=1.062|T=0.6|K=500
----------------------------------------
Step 817
 the, to, how, to, to, how, how, how
chosen= how|entropy=1.183|T=0.6|K=500
----------------------------------------
Step 818
 they, they, they, they, they, их, they, they
chosen= they|entropy=0.159|T=0.6|K=500
----------------------------------------
Step 819
 interact, interact, interact, interact, interact, correspond, interact, interact
chosen= interact|entropy=0.166|T=0.6|K=500
----------------------------------------
Step 820
.,., with, with,., or, with,.
chosen= with|entropy=0.454|T=0.6|K=500
----------------------------------------
[Evaluator after step 820]: GOOD
Step 821
 one, one, one, one, each, each, each, one
chosen= each|entropy=0.512|T=0.6|K=500
----------------------------------------
Step 822
 other, other, other, other, other, other, other, other
chosen= other|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 823
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 824
 The, The, The, The, The, Simple, This, This
chosen= This|entropy=0.519|T=0.6|K=500
----------------------------------------
Step 825
 can, can, can, includes, leads, involves, can, can
chosen= can|entropy=0.786|T=0.6|K=500
----------------------------------------
[Evaluator after step 825]: GOOD
Step 826
 be, be, be, involve, involve, involve, be, be
chosen= be|entropy=0.385|T=0.6|K=500
----------------------------------------
Step 827
 a, done, complex, achieved, a, complex, done, done
chosen= done|entropy=1.059|T=0.6|K=500
----------------------------------------
Step 828
 using, using, using, using, through, using, using, using
chosen= using|entropy=0.485|T=0.6|K=500
----------------------------------------
Step 829
 the, the, the, concepts, concepts, the, the, the
chosen= the|entropy=0.875|T=0.6|K=500
----------------------------------------
Step 830
 addition, addition, principles, principles, principle, law, principles, multiplication
chosen= principles|entropy=1.194|T=0.6|K=500
----------------------------------------
[Evaluator after step 830]: GOOD
Step 831
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 832
 probability, probability, probability, set, probability, probability, probability, probability
chosen= probability|entropy=0.260|T=0.6|K=500
----------------------------------------
Step 833
 theory,,,,, theory,,,,,,, theory
chosen=,|entropy=0.932|T=0.6|K=500
----------------------------------------
Step 834
 such, such, such, such, such, such, such, such
chosen= such|entropy=0.114|T=0.6|K=500
----------------------------------------
Step 835
 as, as, as, as, as, as, as, as
chosen= as|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 835]: GOOD
Step 836
 the, the, the, addition, the, the, the, the
chosen= the|entropy=0.353|T=0.6|K=500
----------------------------------------
Step 837
 addition, multiplication, multiplication, multiplication, multiplication, multiplication, multiplication, addition
chosen= multiplication|entropy=0.425|T=0.6|K=500
----------------------------------------
Step 838
 rule, rule, rule, rule, rule, theorem, rule, rule
chosen= rule|entropy=0.032|T=0.6|K=500
----------------------------------------
Step 839
,,,, and, and, for, for,,,,
chosen=,|entropy=0.961|T=0.6|K=500
----------------------------------------
Step 840
 addition, addition, the, which, addition, addition, addition, which
chosen= addition|entropy=0.393|T=0.6|K=500
----------------------------------------
[Evaluator after step 840]: GOOD
Step 841
 rule, rule, rule, rule, rule, rule, rule, rule
chosen= rule|entropy=0.010|T=0.6|K=500
----------------------------------------
Step 842
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 843
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 844
 conditional, conditional, inclusion, conditional, the, conditional, conditional, combination
chosen= conditional|entropy=0.860|T=0.6|K=500
----------------------------------------
Step 845
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 845]: GOOD
Step 846
.,,,.

,.,.

,.

,.

,.
chosen=.

|entropy=0.519|T=0.6|K=500
----------------------------------------
Step 847
The,**,**,**,**,Each,The,The
chosen=The|entropy=0.713|T=0.6|K=500
----------------------------------------
Step 848
 multiplication, multiplication, multiplication, multiplication, probability, probability, multiplication, multiplication
chosen= multiplication|entropy=0.495|T=0.6|K=500
----------------------------------------
Step 849
 rule, rule, rule, rule, rule, rule, rule, rule
chosen= rule|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 850
 states, states, states, states, states, states, is, states
chosen= is|entropy=0.562|T=0.6|K=500
----------------------------------------
[Evaluator after step 850]: GOOD
Step 851
 used, used, used, used, used, used, used, used
chosen= used|entropy=0.007|T=0.6|K=500
----------------------------------------
Step 852
 when, when, when, when, to, to, to, to
chosen= to|entropy=0.708|T=0.6|K=500
----------------------------------------
Step 853
 find, find, find, calculate, calculate, find, calculate, calculate
chosen= calculate|entropy=0.750|T=0.6|K=500
----------------------------------------
Step 854
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 855
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.003|T=0.6|K=500
----------------------------------------
[Evaluator after step 855]: GOOD
Step 856
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.020|T=0.6|K=500
----------------------------------------
Step 857
 the, two, the, multiple, multiple, the, the, the
chosen= the|entropy=0.691|T=0.6|K=500
----------------------------------------
Step 858
 occurrence, occurrence, intersection, occurrence, intersection, joint, intersection, intersection
chosen= intersection|entropy=0.648|T=0.6|K=500
----------------------------------------
Step 859
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 860
 two, two, two, two, two, two, two, two
chosen= two|entropy=0.041|T=0.6|K=500
----------------------------------------
[Evaluator after step 860]: GOOD
Step 861
 events, or, events, events, events, events, events, independent
chosen= events|entropy=0.260|T=0.6|K=500
----------------------------------------
Step 862
.,,,., occurring,., (,,,.
chosen=,|entropy=0.625|T=0.6|K=500
----------------------------------------
Step 863
 while, while, while, while, while, while, while, the
chosen= while|entropy=0.442|T=0.6|K=500
----------------------------------------
Step 864
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 865
 addition, addition, addition, addition, addition, adoption, addition, addition
chosen= addition|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 865]: GOOD
Step 866
 rule, rule, rule, rule, rule, rule, rule, rule
chosen= rule|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 867
 is, is, is, is, is, is, is, helps
chosen= is|entropy=0.013|T=0.6|K=500
----------------------------------------
Step 868
 used, used, used, used, used, used, used, used
chosen= used|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 869
 to, to, to, to, to, for, to, to
chosen= to|entropy=0.060|T=0.6|K=500
----------------------------------------
Step 870
 calculate, calculate, calculate, calculate, calculate, calculate, calculate, calculate
chosen= calculate|entropy=0.094|T=0.6|K=500
----------------------------------------
[Evaluator after step 870]: GOOD
Step 871
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 872
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 873
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 874
 the, the, the, the, the, the, the, either
chosen= the|entropy=0.135|T=0.6|K=500
----------------------------------------
Step 875
 union, union, union, union, union, union, union, union
chosen= union|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 875]: GOOD
Step 876
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 877
 two, two, two, two, two, another, two, two
chosen= two|entropy=0.010|T=0.6|K=500
----------------------------------------
Step 878
 events, events, events, events, events, events, events, events
chosen= events|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 879
.,.,.,.,.,.,.,.
chosen=.|entropy=0.004|T=0.6|K=500
----------------------------------------
Step 880
 The, The, Conditional, The, Conditional, Logical, Conditional, Conditional
chosen= Conditional|entropy=0.736|T=0.6|K=500
----------------------------------------
[Evaluator after step 880]: GOOD
Step 881
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 882
 is, is, is, deals, considers, is, is, is
chosen= is|entropy=0.518|T=0.6|K=500
----------------------------------------
Step 883
 used, used, a, used, a, important, used, a
chosen= used|entropy=1.343|T=0.6|K=500
----------------------------------------
Step 884
 to, to, to, to, to, to, when, to
chosen= when|entropy=0.500|T=0.6|K=500
----------------------------------------
Step 885
 we, the, we, events, we, the, the, we
chosen= the|entropy=1.079|T=0.6|K=500
----------------------------------------
[Evaluator after step 885]: GOOD
Step 886
 occurrence, occurrence, occurrence, occurrence, probability, occurrence, occurrence, occurrence
chosen= occurrence|entropy=0.093|T=0.6|K=500
----------------------------------------
Step 887
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 888
 one, one, one, one, one, one, one, one
chosen= one|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 889
 event, event, event, event, event, event, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 890
 affects, affects, impacts, affects, affects, affects, affects, affects
chosen= affects|entropy=0.140|T=0.6|K=500
----------------------------------------
[Evaluator after step 890]: GOOD
Step 891
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 892
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 893
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 894
 another, another, another, another, the, the, another, another
chosen= another|entropy=0.047|T=0.6|K=500
----------------------------------------
Step 895
 event, event,.

, event, event, event, event, event
chosen= event|entropy=0.524|T=0.6|K=500
----------------------------------------
[Evaluator after step 895]: GOOD
Step 896
.

, occurring,.

,.

,.

, happening,.

,.


chosen=.

|entropy=0.098|T=0.6|K=500
----------------------------------------
Step 897
**,**,**,These,**,In,**,**
chosen=**|entropy=0.591|T=0.6|K=500
----------------------------------------
Step 898
2,2,2,2,2,2,2,2
chosen=2|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 899
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 900
3,3,2,3,2,2,2,2
chosen=2|entropy=0.352|T=0.6|K=500
----------------------------------------
[Evaluator after step 900]: GOOD
Step 901
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.8|K=400
----------------------------------------
Step 902
4,4,4,4,4,4,4,4
chosen=4|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 903
 Measure, Probability, Measure, Determin, Meeting, Properties, Mathematical, Mathematical
chosen= Mathematical|entropy=0.842|T=0.6|K=500
----------------------------------------
Step 904
 Foundations, Foundations, Foundations, Foundations, Foundations, Foundations, Foundations, Foundations
chosen= Foundations|entropy=0.023|T=0.6|K=500
----------------------------------------
Step 905
 of, of, of, of, of,**

, of, of
chosen= of|entropy=0.082|T=0.6|K=500
----------------------------------------
[Evaluator after step 905]: GOOD
Step 906
 Probability, Probability, Probability, Probability, Probability, Probability, Probability, Probability
chosen= Probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 907
**

,**

, Theory,**

,**

,**

,**

,**


chosen=**

|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 908
The,The,The,Probability,The,The,The,In
chosen=The|entropy=0.425|T=0.6|K=500
----------------------------------------
Step 909
 mathematical, mathematical, mathematical, mathematical, mathematical, mathematical, mathematical, mathematical
chosen= mathematical|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 910
 foundations, foundations, foundation, foundations, foundation, foundations, foundations, foundations
chosen= foundations|entropy=0.576|T=0.6|K=500
----------------------------------------
[Evaluator after step 910]: GOOD
Step 911
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 912
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 913
 are, include, theory, include, are, theory, include, include
chosen= include|entropy=0.835|T=0.6|K=500
----------------------------------------
Step 914
 concepts, concepts, concepts, measure, measure, concepts, measure, concepts
chosen= measure|entropy=0.827|T=0.6|K=500
----------------------------------------
Step 915
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 915]: GOOD
Step 916
,,,,,,,,,,,,,,,
chosen=,|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 917
 which, stochastic, stochastic, which, stochastic, stochastic, which, which
chosen= which|entropy=0.539|T=0.6|K=500
----------------------------------------
Step 918
 provides, provides, provides, provides, provides, provides, provides, is
chosen= provides|entropy=0.062|T=0.6|K=500
----------------------------------------
Step 919
 a, a, a, a, a, a, a, a
chosen= a|entropy=0.135|T=0.6|K=500
----------------------------------------
Step 920
 way, way, rigorous, rigorous, way, way, way, way
chosen= way|entropy=0.791|T=0.6|K=500
----------------------------------------
[Evaluator after step 920]: GOOD
Step 921
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 922
 assign, assign, describe, define, define, cod, assign, define
chosen= assign|entropy=1.000|T=0.6|K=500
----------------------------------------
Step 923
 probabilities, probabilities, probability, probabilities, probabilities, probabilities, probabilities, measures
chosen= probabilities|entropy=0.278|T=0.6|K=500
----------------------------------------
Step 924
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 925
 events, subsets, various, events, sets, sets, sets, sets
chosen= sets|entropy=0.898|T=0.6|K=500
----------------------------------------
[Evaluator after step 925]: GOOD
Step 926
 and, and, and, and,., of, and,.
chosen= and|entropy=0.583|T=0.6|K=500
----------------------------------------
Step 927
 events, events, their, sub, events, subsets, events, spaces
chosen= events|entropy=0.491|T=0.6|K=500
----------------------------------------
Step 928
.,., in,.,.,.,.,.
chosen=.|entropy=0.122|T=0.6|K=500
----------------------------------------
Step 929
 St, In, In, Measure, This, In, St, This
chosen= St|entropy=1.391|T=0.6|K=500
----------------------------------------
Step 930
ochastic,ochastic,ochastic,ochastic,ochastic,ochastic,ochastic,ochastic
chosen=ochastic|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 930]: GOOD
Step 931
 processes, processes, processes, processes, processes, processes, processes, processes
chosen= processes|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 932
,, are,,,,, are, are, are, are
chosen= are|entropy=0.407|T=0.6|K=500
----------------------------------------
Step 933
 mathematical, used, models, discrete, mathematical, mathematical, used, used
chosen= used|entropy=1.034|T=0.6|K=500
----------------------------------------
Step 934
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.010|T=0.6|K=500
----------------------------------------
Step 935
 model, model, model, model, model, model, model, model
chosen= model|entropy=0.086|T=0.6|K=500
----------------------------------------
[Evaluator after step 935]: GOOD
Step 936
 complex, systems, systems, the, random, sequences, systems, continuous
chosen= systems|entropy=1.599|T=0.6|K=500
----------------------------------------
Step 937
 that, that, with, that, that, that, that, that
chosen= that|entropy=0.112|T=0.6|K=500
----------------------------------------
Step 938
 evolve, evolve, are, are, change, are, are, undergo
chosen= are|entropy=1.163|T=0.6|K=500
----------------------------------------
Step 939
 governed, governed, governed, changing, governed, behavior, influenced, probabil
chosen= influenced|entropy=1.346|T=0.6|K=500
----------------------------------------
Step 940
 by, by, by, by, by, by, by, by
chosen= by|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 940]: GOOD
Step 941
 random, random, multiple, random, random, multiple, random, randomness
chosen= random|entropy=0.051|T=0.6|K=500
----------------------------------------
Step 942
 factors, factors, variables, factors, factors, noise, variables, factors
chosen= variables|entropy=0.176|T=0.6|K=500
----------------------------------------
Step 943
.,,, and,.,,,,, and,.
chosen= and|entropy=1.065|T=0.6|K=500
----------------------------------------
Step 944
 their, processes, their, their, random, their, their, can
chosen= their|entropy=0.698|T=0.6|K=500
----------------------------------------
Step 945
 interactions, interactions, interactions, interactions, interactions, interactions, interactions, interactions
chosen= interactions|entropy=0.050|T=0.6|K=500
----------------------------------------
[Evaluator after step 945]: GOOD
Step 946
.,.,.,.,.,.,., over
chosen=.|entropy=0.037|T=0.6|K=500
----------------------------------------
Step 947
 Conditional, Conditional, Conditional, Conditional, Conditional, Conditional, Conditional, Conditional
chosen= Conditional|entropy=0.037|T=0.6|K=500
----------------------------------------
Step 948
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 949
 is, is, is, is, is, refers, is, is
chosen= is|entropy=0.074|T=0.6|K=500
----------------------------------------
Step 950
 an, a, a, often, a, used, essential, a
chosen= essential|entropy=0.533|T=0.6|K=500
----------------------------------------
[Evaluator after step 950]: GOOD
Step 951
 in, in, in, in, in, in, in, in
chosen= in|entropy=0.418|T=0.6|K=500
----------------------------------------
Step 952
 understanding, understanding, calculating, Bayesian, connecting, conditional, understanding, scenarios
chosen= understanding|entropy=0.768|T=0.6|K=500
----------------------------------------
Step 953
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.254|T=0.6|K=500
----------------------------------------
Step 954
 relationship, relationship, relationship, relationship, relationship, relationship, relationship, relationship
chosen= relationship|entropy=0.218|T=0.6|K=500
----------------------------------------
Step 955
 between, between, between, between, between, between, between, between
chosen= between|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 955]: GOOD
Step 956
 different, two, events, events, events, two, events, events
chosen= events|entropy=1.033|T=0.6|K=500
----------------------------------------
Step 957
.

,,,.

, and,.

, and,,,.


chosen=,|entropy=0.833|T=0.6|K=500
----------------------------------------
Step 958
 especially, and, and, and, and, and, and, and
chosen= and|entropy=0.160|T=0.6|K=500
----------------------------------------
Step 959
 it, the, it, it, it, the, it, the
chosen= it|entropy=0.714|T=0.6|K=500
----------------------------------------
Step 960
 plays, allows, plays, is, is, is, allows, plays
chosen= allows|entropy=1.324|T=0.6|K=500
----------------------------------------
[Evaluator after step 960]: GOOD
Step 961
 us, us, us, us, us, for, us, us
chosen= us|entropy=0.297|T=0.6|K=500
----------------------------------------
Step 962
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 963
 calculate, calculate, calculate, represent, calculate, express, calculate, calculate
chosen= calculate|entropy=0.717|T=0.6|K=500
----------------------------------------
Step 964
 the, probabilities, the, the, probabilities, the, the, probabilities
chosen= the|entropy=0.503|T=0.6|K=500
----------------------------------------
Step 965
 probability, probability, probability, likelihood, probability, probability, probability, probability
chosen= probability|entropy=0.067|T=0.6|K=500
----------------------------------------
[Evaluator after step 965]: GOOD
Step 966
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 967
 one, one, a, the, the, an, one, events
chosen= one|entropy=0.824|T=0.6|K=500
----------------------------------------
Step 968
 event, event, event, event, event, event, event, event
chosen= event|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 969
 given, given, given, occurring, given, given, given, given
chosen= given|entropy=0.312|T=0.6|K=500
----------------------------------------
Step 970
 the, that, the, the, the, that, the, the
chosen= the|entropy=0.054|T=0.6|K=500
----------------------------------------
[Evaluator after step 970]: GOOD
Step 971
 probability, occurrence, probability, information, occurrence, probability, probability, probability
chosen= probability|entropy=0.656|T=0.6|K=500
----------------------------------------
Step 972
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 973
 another, another, another, another, another, another, another, another
chosen= another|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 974
.

,.

,.

, event,.

,.

,.

,.


chosen=.

|entropy=0.213|T=0.6|K=500
----------------------------------------
Step 975
**,These,**,**,These,**,It,**
chosen=It|entropy=0.855|T=0.6|K=500
----------------------------------------
[Evaluator after step 975]: GOOD
Step 976
 is, is, is, is, is, is, is, is
chosen= is|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 977
 important, important, important, virtually, important, important, important, important
chosen= important|entropy=0.552|T=0.6|K=500
----------------------------------------
Step 978
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 979
 note, note, note, realize, note, emphasize, note, remind
chosen= note|entropy=0.240|T=0.6|K=500
----------------------------------------
Step 980
 that, that, that, that, that, that, that, that
chosen= that|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 980]: GOOD
Step 981
 the, probability, probability, probability, probability, these, probability, probability
chosen= probability|entropy=0.360|T=0.6|K=500
----------------------------------------
Step 982
 theory, theory, theory, is, theory, theory, theory, theory
chosen= theory|entropy=0.020|T=0.6|K=500
----------------------------------------
Step 983
 is, is, is, provides, is, is, is, is
chosen= is|entropy=0.062|T=0.6|K=500
----------------------------------------
Step 984
 built, a, built, a, built, built, a, a
chosen= a|entropy=0.853|T=0.6|K=500
----------------------------------------
Step 985
 rigorous, mathematical, mathematical, well, well, subject, mathematical, complex
chosen= mathematical|entropy=1.520|T=0.6|K=500
----------------------------------------
[Evaluator after step 985]: GOOD
Step 986
 framework, discipline, theory, field, theory, foundation, framework, theory
chosen= framework|entropy=1.181|T=0.6|K=500
----------------------------------------
Step 987
 that, that, that, that, that, that, that,,
chosen= that|entropy=0.363|T=0.6|K=500
----------------------------------------
Step 988
 uses, can, combines, can, deals, combines, can, has
chosen= can|entropy=1.591|T=0.6|K=500
----------------------------------------
Step 989
 be, be, be, be, be, be, be, be
chosen= be|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 990
 used, applied, applied, used, used, used, applied, used
chosen= applied|entropy=0.772|T=0.6|K=500
----------------------------------------
[Evaluator after step 990]: GOOD
Step 991
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.164|T=0.6|K=500
----------------------------------------
Step 992
 various, various, various, various, a, a, a, various
chosen= a|entropy=0.775|T=0.6|K=500
----------------------------------------
Step 993
 wide, wide, wide, wide, wide, wide, wide, wide
chosen= wide|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 994
 range, range, range, range, range, range, range, range
chosen= range|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 995
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 995]: GOOD
Step 996
 real, real, scientific, real, disciplines, problems, fields, scientific
chosen= fields|entropy=1.769|T=0.6|K=500
----------------------------------------
Step 997
,,,,,,,,,,,,,,.
chosen=,|entropy=0.102|T=0.6|K=500
----------------------------------------
Step 998
 including, from, including, including, from, from, from, from
chosen= from|entropy=0.834|T=0.6|K=500
----------------------------------------
Step 999
 physics, physics, physics, physics, physics, finance, finance, statistics
chosen= finance|entropy=1.258|T=0.6|K=500
----------------------------------------
Step 1000
 and, to, and, to, and, to, to, and
chosen= to|entropy=0.557|T=0.6|K=500
----------------------------------------
[Evaluator after step 1000]: GOOD
Step 1001
 engineering, physics, engineering, machine, physics, statistics, physics, biology
chosen= physics|entropy=1.213|T=0.6|K=500
----------------------------------------
Step 1002
,,,, to, to,,, and,,, to
chosen=,|entropy=1.003|T=0.6|K=500
----------------------------------------
Step 1003
 and, and, mathematics, as, and, and, and, and
chosen= and|entropy=0.220|T=0.6|K=500
----------------------------------------
Step 1004
 it, it, it, to, it, beyond, it, it
chosen= it|entropy=0.409|T=0.6|K=500
----------------------------------------
Step 1005
 provides, has, provides, plays, provides, plays, provides, provides
chosen= provides|entropy=0.733|T=0.6|K=500
----------------------------------------
[Evaluator after step 1005]: GOOD
Step 1006
 tools, the, a, a, a, a, a, powerful
chosen= a|entropy=0.200|T=0.6|K=500
----------------------------------------
Step 1007
 systematic, foundation, powerful, means, systematic, comparison, way, rigorous
chosen= way|entropy=1.702|T=0.6|K=500
----------------------------------------
Step 1008
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 1009
 analyze, analyze, model, quantify, analyze, analyze, model, model
chosen= model|entropy=1.014|T=0.6|K=500
----------------------------------------
Step 1010
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.066|T=0.6|K=500
----------------------------------------
[Evaluator after step 1010]: GOOD
Step 1011
 analyze, analyze, analyze, analyze, analyze, analyze, analyze, analyze
chosen= analyze|entropy=0.043|T=0.6|K=500
----------------------------------------
Step 1012
 complex, uncertain, phenomena, uncertain, uncertain,-random, uncertain, uncertain
chosen= uncertain|entropy=0.814|T=0.6|K=500
----------------------------------------
Step 1013
 outcomes, outcomes, outcomes, systems, outcomes, outcomes, outcomes, and
chosen= outcomes|entropy=0.437|T=0.6|K=500
----------------------------------------
Step 1014
.

,.

,.

,.

,.

,.

,.

,.


chosen=.

|entropy=0.230|T=0.6|K=500
----------------------------------------
Step 1015
**,**,**,**,**,**,**,**
chosen=**|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 1015]: GOOD
Step 1016
2,2,2,2,2,2,2,2
chosen=2|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 1017
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.7|K=200
----------------------------------------
Step 1018
3,3,2,3,3,3,3,3
chosen=3|entropy=0.061|T=0.6|K=500
----------------------------------------
Step 1019
 Applications, Applications, Applications, Applications, Applications, Ge, Applications, Applications
chosen= Applications|entropy=0.070|T=0.6|K=500
----------------------------------------
Step 1020
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.035|T=0.6|K=500
----------------------------------------
[Evaluator after step 1020]: GOOD
Step 1021
 Probability, Probability, Probability, Probability, Probability, Probability, Probability, Probability
chosen= Probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1022
 Theory, Theory, Theory, Theory, Theory, Theory, Theory, Theory
chosen= Theory|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 1023
**

,**

,**

, in,**

,**

,**

,**


chosen=**

|entropy=0.052|T=0.6|K=500
----------------------------------------
Step 1024
Probability,Probability,Probability,Probability,The,Probability,Probability,Probability
chosen=Probability|entropy=0.196|T=0.6|K=500
----------------------------------------
Step 1025
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1025]: GOOD
Step 1026
 has, is, has, has, has, has, has, has
chosen= has|entropy=0.161|T=0.6|K=500
----------------------------------------
Step 1027
 numerous, numerous, broad, wide, been, numerous, numerous, numerous
chosen= numerous|entropy=0.972|T=0.6|K=500
----------------------------------------
Step 1028
 applications, applications, applications, applications, applications, applications, applications, applications
chosen= applications|entropy=0.037|T=0.6|K=500
----------------------------------------
Step 1029
 in, in, in, in, in, in, in, in
chosen= in|entropy=0.021|T=0.6|K=500
----------------------------------------
Step 1030
 various, various, various, various, various, different, various, various
chosen= various|entropy=0.229|T=0.6|K=500
----------------------------------------
[Evaluator after step 1030]: GOOD
Step 1031
 fields, fields, fields, fields, fields, fields, fields, fields
chosen= fields|entropy=0.113|T=0.6|K=500
----------------------------------------
Step 1032
,,.,,,,,.,.,,,,
chosen=,|entropy=0.720|T=0.6|K=500
----------------------------------------
Step 1033
 including, including, making, including, making, including, including, including
chosen= including|entropy=0.250|T=0.6|K=500
----------------------------------------
Step 1034
 finance, finance, finance, finance, finance,:

, finance, finance
chosen= finance|entropy=0.137|T=0.6|K=500
----------------------------------------
Step 1035
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1035]: GOOD
Step 1036
 healthcare, healthcare, healthcare, healthcare, healthcare, healthcare, healthcare, statistics
chosen= healthcare|entropy=0.024|T=0.6|K=500
----------------------------------------
Step 1037
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1038
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.066|T=0.6|K=500
----------------------------------------
Step 1039
 engineering, engineering, engineering, engineering, engineering, engineering, engineering, engineering
chosen= engineering|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1040
.,.,.,.,.,.,.,.
chosen=.|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 1040]: GOOD
Step 1041
 In, In, In, In, In, It, In, In
chosen= In|entropy=0.095|T=0.6|K=500
----------------------------------------
Step 1042
 finance, finance, finance, finance, finance, finance, finance, finance
chosen= finance|entropy=0.014|T=0.6|K=500
----------------------------------------
Step 1043
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1044
 it, probability, probability, probability, probability, probability, probability, it
chosen= probability|entropy=0.134|T=0.6|K=500
----------------------------------------
Step 1045
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.037|T=0.6|K=500
----------------------------------------
[Evaluator after step 1045]: GOOD
Step 1046
 is, is, is, is, is, is, is, is
chosen= is|entropy=0.011|T=0.6|K=500
----------------------------------------
Step 1047
 used, used, used, used, used, used, used, used
chosen= used|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 1048
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.012|T=0.6|K=500
----------------------------------------
Step 1049
 model, model, model, model, assess, model, model, model
chosen= model|entropy=0.196|T=0.6|K=500
----------------------------------------
Step 1050
 stock, the, stock, stock, the, the, and, and
chosen= and|entropy=0.610|T=0.6|K=500
----------------------------------------
[Evaluator after step 1050]: GOOD
Step 1051
 analyze, analyze, analyze, analyze, assess, forecasting, analyze, analyze
chosen= analyze|entropy=0.178|T=0.6|K=500
----------------------------------------
Step 1052
 the, stock, stock, financial, financial, stock, the, stock
chosen= the|entropy=0.844|T=0.6|K=500
----------------------------------------
Step 1053
 performance, pricing, behavior, behavior, behavior, stock, behavior, pricing
chosen= behavior|entropy=0.550|T=0.6|K=500
----------------------------------------
Step 1054
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1055
 stock, financial, financial, stock, stock, investment, financial, stock
chosen= financial|entropy=0.419|T=0.6|K=500
----------------------------------------
[Evaluator after step 1055]: GOOD
Step 1056
 markets, markets, instruments, markets, markets, markets, markets, markets
chosen= markets|entropy=0.098|T=0.6|K=500
----------------------------------------
Step 1057
,,,,,,,,,, and,,,,
chosen=,|entropy=0.573|T=0.6|K=500
----------------------------------------
Step 1058
 making, assess, hedge, making, making, determine, making, where
chosen= making|entropy=1.821|T=0.6|K=500
----------------------------------------
Step 1059
 it, it, predictions, it, it, predictions, it, it
chosen= it|entropy=0.092|T=0.6|K=500
----------------------------------------
Step 1060
 an, an, an, a, a, an, an, an
chosen= an|entropy=0.829|T=0.6|K=500
----------------------------------------
[Evaluator after step 1060]: GOOD
Step 1061
 essential, essential, essential, essential, essential, important, essential, essential
chosen= essential|entropy=0.314|T=0.6|K=500
----------------------------------------
Step 1062
 tool, tool, tool, tool, tool, tool, tool, component
chosen= tool|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 1063
 for, for, for, for, for, for, for, for
chosen= for|entropy=0.129|T=0.6|K=500
----------------------------------------
Step 1064
 risk, investors, investors, investors, investors, decision, risk, pricing
chosen= risk|entropy=0.891|T=0.6|K=500
----------------------------------------
Step 1065
 assessment, management, management, assessment, assessment, assessment, assessment, assessment
chosen= assessment|entropy=0.515|T=0.6|K=500
----------------------------------------
[Evaluator after step 1065]: GOOD
Step 1066
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.021|T=0.6|K=500
----------------------------------------
Step 1067
 investment, investment, investment, decision, decision, portfolio, investment, portfolio
chosen= investment|entropy=0.281|T=0.6|K=500
----------------------------------------
Step 1068
 decisions, decisions, decision, planning, decisions, decisions, planning, decisions
chosen= planning|entropy=0.543|T=0.6|K=500
----------------------------------------
Step 1069
.,.,.,.,.,.,.,.
chosen=.|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1070
 In, In, In, In, In, In, In, In
chosen= In|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 1070]: GOOD
Step 1071
 healthcare, healthcare, healthcare, healthcare, healthcare, healthcare, healthcare, healthcare
chosen= healthcare|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1072
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1073
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 1074
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1075
 is, is, helps, is, is, is, is, is
chosen= is|entropy=0.184|T=0.6|K=500
----------------------------------------
[Evaluator after step 1075]: GOOD
Step 1076
 used, used, used, used, used, used, used, used
chosen= used|entropy=0.021|T=0.6|K=500
----------------------------------------
Step 1077
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.063|T=0.6|K=500
----------------------------------------
Step 1078
 model, study, help, guide, evaluate, assess, analyze, model
chosen= analyze|entropy=1.493|T=0.6|K=500
----------------------------------------
Step 1079
 medical, and, data, patient, the, experimental, the, and
chosen= the|entropy=1.439|T=0.6|K=500
----------------------------------------
Step 1080
 effectiveness, frequency, risk, risk, outcomes, outcomes, effects, risk
chosen= effects|entropy=1.805|T=0.6|K=500
----------------------------------------
[Evaluator after step 1080]: GOOD
Step 1081
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1082
 treatments, treatments, treatments, treatments, treatments, medical, treatments, treatments
chosen= treatments|entropy=0.885|T=0.6|K=500
----------------------------------------
Step 1083
 and, and, and, on, on, and, and, and
chosen= and|entropy=0.415|T=0.6|K=500
----------------------------------------
Step 1084
 to, better, outcomes, interventions, predict, management, to, outcomes
chosen= to|entropy=1.438|T=0.6|K=500
----------------------------------------
Step 1085
 make, develop, assess, evaluate, design, support, assess, evaluate
chosen= assess|entropy=1.794|T=0.6|K=500
----------------------------------------
[Evaluator after step 1085]: GOOD
Step 1086
 the, the, the, the, the, the, the, the
chosen= the|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 1087
 success, likelihood, effectiveness, likelihood, likelihood, best, effectiveness, likelihood
chosen= effectiveness|entropy=0.627|T=0.6|K=500
----------------------------------------
Step 1088
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.009|T=0.6|K=500
----------------------------------------
Step 1089
 health, medical, interventions, treatments, medical, clinical, medical, medical
chosen= medical|entropy=0.412|T=0.6|K=500
----------------------------------------
Step 1090
 interventions, interventions, interventions, interventions, interventions, interventions, interventions, interventions
chosen= interventions|entropy=0.214|T=0.6|K=500
----------------------------------------
[Evaluator after step 1090]: GOOD
Step 1091
.,.,.,.,.,.,.,.


chosen=.|entropy=0.086|T=0.6|K=500
----------------------------------------
Step 1092
 In, In, In, In, In, In, In, In
chosen= In|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1093
 engineering, engineering, engineering, engineering, engineering, engineering, engineering, engineering
chosen= engineering|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1094
,,,,,,,,,, and,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1095
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.011|T=0.6|K=500
----------------------------------------
[Evaluator after step 1095]: GOOD
Step 1096
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1097
 is, is, is, is, is, plays, is, is
chosen= is|entropy=0.023|T=0.6|K=500
----------------------------------------
Step 1098
 used, used, used, used, used, used, used, used
chosen= used|entropy=0.004|T=0.6|K=500
----------------------------------------
Step 1099
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.003|T=0.6|K=500
----------------------------------------
Step 1100
 design, model, model, assess, model, model, model, model
chosen= model|entropy=0.515|T=0.6|K=500
----------------------------------------
[Evaluator after step 1100]: GOOD
Step 1101
 and, and, and, and, and, and, and, and
chosen= and|entropy=0.188|T=0.6|K=500
----------------------------------------
Step 1102
 analyze, analyze, analyze, analyze, analyze, analyze, analyze, predict
chosen= analyze|entropy=0.038|T=0.6|K=500
----------------------------------------
Step 1103
 systems, various, systems, systems, systems, the, the, systems
chosen= the|entropy=0.742|T=0.6|K=500
----------------------------------------
Step 1104
 behavior, reliability, behavior, performance, behavior, behaviors, behavior, behavior
chosen= behavior|entropy=0.365|T=0.6|K=500
----------------------------------------
Step 1105
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1105]: GOOD
Step 1106
 engineering, systems, complex, complex, systems, complex, systems, systems
chosen= systems|entropy=0.505|T=0.6|K=500
----------------------------------------
Step 1107
 and, and,,, that, and,,, and, that
chosen= and|entropy=1.158|T=0.6|K=500
----------------------------------------
Step 1108
 to, the, processes, processes, to, processes, processes, to
chosen= processes|entropy=0.668|T=0.6|K=500
----------------------------------------
Step 1109
.

,,,.

,.

,.

,,,,, that
chosen=,|entropy=0.699|T=0.6|K=500
----------------------------------------
Step 1110
 helping, making, which, aiding, making, enabling, helping, making
chosen= helping|entropy=1.346|T=0.6|K=500
----------------------------------------
[Evaluator after step 1110]: GOOD
Step 1111
 to, to, to, to, to, in, to, to
chosen= to|entropy=0.211|T=0.6|K=500
----------------------------------------
Step 1112
 predict, improve, ensure, assess, identify, manage, predict, improve
chosen= predict|entropy=1.575|T=0.6|K=500
----------------------------------------
Step 1113
 and, their, their, and, and, and, and, and
chosen= and|entropy=0.605|T=0.6|K=500
----------------------------------------
Step 1114
 optimize, improve, improve, manage, improve, improve, improve, improve
chosen= improve|entropy=0.978|T=0.6|K=500
----------------------------------------
Step 1115
 the, the, the, the, the, the, the, performance
chosen= the|entropy=0.626|T=0.6|K=500
----------------------------------------
[Evaluator after step 1115]: GOOD
Step 1116
 performance, performance, performance, performance, performance, performance, performance, success
chosen= performance|entropy=0.071|T=0.6|K=500
----------------------------------------
Step 1117
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.008|T=0.6|K=500
----------------------------------------
Step 1118
 real, these, these, these, systems, these, these, complex
chosen= these|entropy=0.378|T=0.6|K=500
----------------------------------------
Step 1119
 systems, systems, systems, systems, systems, systems, systems, systems
chosen= systems|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1120
.

,.

,.

,.

,.

, uniquely,.

,.


chosen=.

|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1120]: GOOD
Step 1121
The,**,The,**,These,The,The,Probability
chosen=The|entropy=1.527|T=0.6|K=500
----------------------------------------
Step 1122
 applications, applications, application, applications, statistical, statistical, applications, application
chosen= applications|entropy=0.943|T=0.6|K=500
----------------------------------------
Step 1123
 of, of, of, of, of, of, of, of
chosen= of|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1124
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1125
 theory, theory, theory, theory, theory, theory, theory, theory
chosen= theory|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1125]: GOOD
Step 1126
 are, are, are, extend, are, are, are, are
chosen= are|entropy=0.339|T=0.6|K=500
----------------------------------------
Step 1127
 vast, not, not, not, diverse, diverse, not, not
chosen= not|entropy=1.218|T=0.6|K=500
----------------------------------------
Step 1128
 limited, limited, limited, limited, limited, limited, limited, limited
chosen= limited|entropy=0.002|T=0.6|K=500
----------------------------------------
Step 1129
 to, to, to, to, to, to, to, to
chosen= to|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1130
 these, these, these, these, these, these, these, these
chosen= these|entropy=0.008|T=0.6|K=500
----------------------------------------
[Evaluator after step 1130]: GOOD
Step 1131
 fields, fields, fields, sectors, fields, fields, fields, sectors
chosen= fields|entropy=0.057|T=0.6|K=500
----------------------------------------
Step 1132
;,;,,,;,;,;,;,,
chosen=;|entropy=0.615|T=0.6|K=500
----------------------------------------
Step 1133
 it, they, they, they, they, it, it, they
chosen= it|entropy=0.591|T=0.6|K=500
----------------------------------------
Step 1134
 is, has, has, is, is, has, is, is
chosen= is|entropy=0.527|T=0.6|K=500
----------------------------------------
Step 1135
 also, used, a, also, also, widely, used, used
chosen= used|entropy=1.074|T=0.6|K=500
----------------------------------------
[Evaluator after step 1135]: GOOD
Step 1136
 in, in, in, widely, in, ubiqu, in, in
chosen= in|entropy=0.006|T=0.6|K=500
----------------------------------------
Step 1137
 many, many, a, a, many, fields, many, many
chosen= many|entropy=0.686|T=0.6|K=500
----------------------------------------
Step 1138
 other, other, other, other, other, other, other, other
chosen= other|entropy=0.372|T=0.6|K=500
----------------------------------------
Step 1139
 areas, areas, areas, domains, areas, areas, areas, areas
chosen= areas|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 1140
,, as, to, as,,,,, as, as
chosen= as|entropy=0.770|T=0.6|K=500
----------------------------------------
[Evaluator after step 1140]: GOOD
Step 1141
 well, well, well, well, well, well, well, well
chosen= well|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1142
.,.,.,.,.,.,.,.
chosen=.|entropy=0.127|T=0.6|K=500
----------------------------------------
Step 1143
 For, For, For, It, It, Probability, For, For
chosen= For|entropy=1.194|T=0.6|K=500
----------------------------------------
Step 1144
 example, example, example, example, example, example, example, example
chosen= example|entropy=0.074|T=0.6|K=500
----------------------------------------
Step 1145
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
[Evaluator after step 1145]: GOOD
Step 1146
 in, in, in, in, in,It, in, in
chosen= in|entropy=0.076|T=0.6|K=500
----------------------------------------
Step 1147
 computer, statistical, machine, statistics, machine, computer, statistics, computer
chosen= statistics|entropy=1.021|T=0.6|K=500
----------------------------------------
Step 1148
,,,,,,,,,,,,,,,
chosen=,|entropy=0.001|T=0.6|K=500
----------------------------------------
Step 1149
 probability, probability, probability, probability, probability, probability, probability, probability
chosen= probability|entropy=0.005|T=0.6|K=500
----------------------------------------
Step 1150
 theory, theory, theory, theory, theory, theories, theory, theory
chosen= theory|entropy=0.002|T=0.6|K=500
----------------------------------------
[Evaluator after step 1150]: GOOD
Step 1151
 is, provides, provides, provides, provides, is, is, is
chosen= is|entropy=0.751|T=0.6|K=500
----------------------------------------
Chapter 2: Deep Mathematics of Probability Theory

In this chapter, we will explore the fundamental concepts of probability theory, focusing on its mathematical structure and its applications in various fields. Probability theory is a branch of mathematics that deals with the modeling of random phenomena and the study of probabilities associated with those phenomena. It is a powerful tool for understanding and predicting outcomes that are uncertain or variable.

The chapter will cover the basic definitions and concepts of probability, such as the probability of an event, the probability distribution, and the probability of multiple events. It will also delve into the mathematical foundations of probability, including concepts such as measure theory, stochastic processes, and conditional probability.

The chapter will also touch upon the applications of probability theory in real-world scenarios, such as in finance, healthcare, and engineering. It will provide an overview of the statistical methods used in probability theory, including hypothesis testing and confidence intervals.

In addition to the mathematical content, the chapter will also touch upon the importance of probability theory in various fields and its impact on scientific research and decision-making. It will encourage readers to explore the mathematical structure of probability theory and its relevance in their own lives.

We will also provide some examples and exercises to help reinforce the concepts discussed in the chapter. The chapter is designed to be comprehensive and engaging, with a focus on the mathematical foundations and applications of probability theory.

The chapter will conclude by summarizing the key points and presenting a clear understanding of the fundamental concepts of probability theory.

I will be writing this chapter in a formal and academic tone, ensuring that the content is both comprehensive and well-structured. I will also make sure to provide practical examples and exercises to illustrate the concepts.

I will not use any markdown or formatting, but will write in a clear and concise manner, with appropriate headings and sections.

Now, let me proceed with writing the chapter.
**Chapter 2: Deep Mathematics of Probability Theory**

**2.1 Introduction to Probability Theory**

Probability theory is a fundamental branch of mathematics that deals with the study of random phenomena. It provides a framework for modeling and analyzing uncertain outcomes, making it an essential tool for various scientific disciplines. Probability theory is built upon the concepts of probability, probability distribution, and stochastic processes. These mathematical structures allow us to quantify the likelihood of different outcomes and assess the probabilities associated with complex systems.

In this chapter, we will explore the mathematical foundations and applications of probability theory. We will begin by discussing the basic concepts of probability, such as the probability of an event, the probability distribution, and the probability of multiple events. We will also delve into the mathematical foundations of probability, including concepts such as measure theory, stochastic processes, and conditional probability.

**2.2 Probability Concepts**

**2.2.1 Probability of an Event**

In probability theory, the probability of an event is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Mathematically, this can be expressed as:

$$
P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
$$

This concept is fundamental in understanding how events can occur and predict their likelihoods. The probability of an event is a measure of how likely it is to occur, ranging from 0 (impossible) to 1 (certainty).

**2.2.2 Probability Distribution**

A probability distribution is a function that assigns probabilities to each possible outcome in a random experiment. This function can be continuous or discrete, depending on the nature of the experiment. For example, a continuous probability distribution assigns probabilities to a range of values, while a discrete probability distribution assigns probabilities to a finite set of values.

The concept of probability distribution is crucial in understanding the behavior of random variables and how they relate to each other. A random variable can have a probability distribution that is continuous or discrete, and the properties of these distributions can be used to describe and analyze the behavior of random processes.

**2.2.3 Probability of Multiple Events**

When dealing with multiple events, it is important to consider the probabilities of each event occurring independently and how they interact with each other. This can be done using the principles of probability, such as the multiplication rule, addition rule, and conditional probability.

The multiplication rule is used to calculate the probability of the intersection of two events, while the addition rule is used to calculate the probability of the union of two events. Conditional probability is used when the occurrence of one event affects the probability of another event.

**2.2.4 Mathematical Foundations of Probability**

The mathematical foundations of probability include measure theory, which provides a way to assign probabilities to sets and events. Stochastic processes are used to model systems that are influenced by random variables and their interactions. Conditional probability is essential in understanding the relationship between events, and it allows us to calculate the probability of one event given the probability of another.

It is important to note that probability theory is a mathematical framework that can be applied to a wide range of fields, from finance to physics, and it provides a way to model and analyze uncertain outcomes.

**2.3 Applications of Probability Theory**

Probability theory has numerous applications in various fields, including finance, healthcare, and engineering. In finance, probability theory is used to model and analyze the behavior of financial markets, making it an essential tool for risk assessment and investment planning. In healthcare, probability theory is used to analyze the effects of treatments and to assess the effectiveness of medical interventions. In engineering, probability theory is used to model and analyze the behavior of systems and processes, helping to predict and improve the performance of these systems.

The applications of probability theory are not limited to these fields; it is used in many other areas as well. For example, in statistics, probability theory is