Hi there! 👋 I am a student currently preparing for the UPSC Indian Statistical Service (ISS) and the Indian Statistical Institute (ISI) entrance exams.
If you are also preparing for these exams, you already know how frustrating it can be to find detailed, rigorous solutions for subjective statistics papers. Most resources just give the final numerical answer, but that doesn't help us understand how to write a proper mathematical proof for the examiners.
I created this repository to document my own study notes, solve these tough papers step-by-step, and share them in hopes that they help fellow aspirants out!
In advanced subjective examinations (especially UPSC ISS and ISI), arriving at the correct final answer is only a fraction of the battle. Examiners grade us based on our mathematical maturity, logical flow, and strict adherence to theoretical assumptions.
Here is how I structure the solutions in this repository to maximize learning and marks:
- 🧠 Approach & Key Concepts: Before jumping into the algebra, I start every solution by explaining why a specific method is chosen. I try to identify the core statistical framework upfront (e.g., Markov Chains, Asymptotic Theory, UMVUE).
- ✍️ Step-by-Step Derivations: I don't skip steps. I make sure to explicitly verify assumptions (like proving zero-covariance before claiming independence in Multivariate Normals) and systematically construct logical bounds.
- 💡 Examiner Insights: I highlight exactly what the grading rubrics look for, making sure to explicitly name the theorems we use (e.g., Neyman-Pearson Lemma, Glivenko-Cantelli Theorem, Continuous Mapping Theorem, Rayleigh Quotients).
I am actively updating this space. Currently, I have uploaded comprehensive solutions for the following subjective papers:
🔗 Click here to view the ISI JRF STB 2026 Solutions
- Key Topics Covered: Real Analysis (Monotone Convergence, limit inferiors), Matrix Theory (idempotency, trace-rank equivalence), Combinatorics (Chromatic Polynomials), and Advanced Inference (Lehmann-Scheffé, Neyman-Pearson Randomized Tests).
🔗 Click here to view the ISI STA 2025 Solutions
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Key Topics Covered: Uniform convergence (
$\epsilon-\delta$ proofs), Linear Algebra (Rank-Nullity intersections, Rayleigh Quotients), Discrete Probability (Negative Binomial frameworks), and Maximum Likelihood Estimation with bounded multidimensional supports.
🔗 Click here to view the ISI STB 2025 Solutions
- Key Topics Covered: Stochastic Processes (Joint Markov Chains & Periodicity), Asymptotic Theory (Delta Method, Weak Law of Large Numbers), Multivariate Normal distributions (Craig's Theorem for quadratic forms), Exact Conditional Hypothesis Testing, and Design of Experiments (Lagrange Multiplier allocations).
If you find these notes helpful, feel free to use them for your own revision. Let's crack these exams together!
Happy studying, and best of luck with your preparation!