[mle] Update lecture with latest code and style

[kp992]

Updates the mle lecture:

• Removed all the old code and replaced with JAX.
• Removed numpy dependency completely.
• Fixed some typos.

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[mmcky]

Thanks @kp992 I have left some minor suggestions and a question re: use of in-built methods.

[HumphreyYang]

Many thanks @kp992! Other than @mmcky's comment, this looks good to me!

[mmcky]

thanks @kp992 I see my comment is now resolved in 511f044

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[jstac]

Many thanks @kp992 , this looks great. So nice to see autodiff at work!

@kp992 @mmcky @HumphreyYang We should try hard to stick to 80 characters per line so that the code fits neatly on the page in html and pdf. It would be good to catch this in PRs when possible.

[kp992]

We should try hard to stick to 80 characters per line so that the code fits neatly on the page in html and pdf

I use jupyter_black auto-formatter while updating the notebook. We just need to add the code block in the start:

import jupyter_black
jupyter_black.load()

I see that by default it uses 88 chars but we can change that to 80:

jupyter_black.load(line_length=80)

[jstac]

Thanks @kp992 !

[mmcky]

thanks @kp992, @jstac and @HumphreyYang. LGTM.