[prob_dist] Editorial Comments

Feedback from @longye-tian (Thanks!)

Code

[x] Give some motivations to use different probability distributions
[x] "One simple example is the uniform distribution, where $p(x_i) = 1/n$ for all $i$ "- > "One simple example is the uniform distribution, where $p(x_i) = 1/n$ for all $n$"
[x] Add some explanations to randint in scipy (by adding a link).
[x] Unify : after the sentence before the code
[x] Unify "PDF" to "PMF" in discrete cases.
[ ] add labels for x and y axis.
[x] The CDF jumps up by $p(x_i)$ and $x_i$.
[x] Update Bernoulli distribution section (@longye-tian) #403.
[x] the number of successes in $n$ independent trials with success probability $\theta$ -> the probability of successes in $n$ independent trials with success probability $\theta$.
[x] "Continuous distributions are represented by a density function" -> "Continuous distributions are represented by a probability density function (PDF)"
[x] "the set of all numbers" -> "the set of all real numbers"
[x] $a \leq b$ -> $a < b$ or change the probability distribution functions.
[x] "We can obtain the moments, PDF and CDF of the normal density as follows" -> "We can obtain the moments, PDF and CDF of the log-normal density as follows"

Comments by @mbek0605:

[x] Bernoulli is a distribution for only two outcomes - make that more clear
[ ] Economic examples for the distributions(?) (Poisson, for example, - useful for calculating the odds of a certain event, or a link to another lecture where it is used / wikipedia)
[ ] Comparison between distributions
[ ] Use case in economics and examples
[ ] We could have the empirical distributions first and then go on to the theoretical distributions (switch the order of the lectures)
[ ] Idea: summary table at the end (mean, variance, cdf and pdf of each one)
[ ] "The the expectation of Poisson distribution" -> "The expectation of Poisson distribution"