[lln_clt] Editorial Comments

[HumphreyYang]

Comments by @SylviaZhaooo:

Content

• introduce what is $n$ -- in the first example is the number of coins being flipped
• Add a link for violin plot in lecture 16
• The LLN fails to hold here because the assumption $\mathbb E|X| = \infty$ is violated by the Cauchy distribution. -> $\mathbb E|X| < \infty$
• state Gaussian distribution is Normal distribution in text
• above1 -> above

Comments by @pgrosser1:

Code

• update the code X = st.bernoulli.rvs(p) to show they are draws (so we should generate the draws, 10 of them) and link to wikipedia article around independent/quasi-independent.
• In section 17.2.4 perhaps add n=1, n=10 steps with an higher variance.

Content

• consider promoting the theory at the end 17.2.1 above the simulations(?) -- could make it clear and use the code as confirmation. But does a good job of providing intuition. Provide some context around Equation 17.1
• In 17.2.4 -- improve clarity around the loop 1 to 3 (sample of sample means) -- less vague language (use algorithm environment from sphinx-proof)
• In 17.2.4 remove the plot of the histogram in section (keep the violin plots and refer to these plots from the CLT section)
• @pgrosser1 mentioned this paper https://www.jstor.org/stable/43601172?seq=18 (example of Cauchy distribution)

[mmcky]

@longye-tian would you be able to take a pass at the comments by @pgrosser1?