[prob_dist] Editorial Comments

[HumphreyYang]

Feedback from @longye-tian (Thanks!)

Code

• Remove redundant code in the Poisson distribution simulation

Content

• Give some motivations to use different probability distributions
• "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 $n$"
• Add some explanations to randint in scipy (by adding a link).
• Unify : after the sentence before the code
• Unify "PDF" to "PMF" in discrete cases.
• add labels for x and y axis.
• The CDF jumps up by $p(x_i)$ and $x_i$.
• Update Bernoulli distribution section (@longye-tian) [prob_dist] Bernoulli distribution section - editorial suggestions #403.
• the number of successes in $n$
  independent trials with success probability $\theta$ -> the probability of successes in $n$
  independent trials with success probability $\theta$.
• "Continuous distributions are represented by a density function" -> "Continuous distributions are represented by a probability density function (PDF)"
• "the set of all numbers" -> "the set of all real numbers"
• $a \leq b$ -> $a < b$ or change the probability distribution functions.
• "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:

Content

• 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"

Code

• label x,y axis in figures
• add mystnb figures wrappers

[longye-tian]

This issue is closed and followed up by #530