[lln_clt] Editorial Comments

Comments by @SylviaZhaooo:

Content

[x] introduce what is $n$ -- in the first example is the number of coins being flipped
[ ] Let $\mu$ denote the common mean of this sample -> population mean.
[x] Add a link for violin plot in lecture 16
[x] The LLN fails to hold here because the assumption $\mathbb E|X| = \infty$ is violated by the Cauchy distribution. -> $\mathbb E|X| < \infty$
[x] state Gaussian distribution is Normal distribution in text
[ ] Show CLT does not hold as well in the two sections breaking LLN
[x] above1 -> above

Comments by @pgrosser1:

[ ] 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.

[ ] 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)