1. Central Limit Theorem for Roll of a Fair Dice: In this .do file (created September 2023 using STATA 17), I show:

   • How to take 100,000 random i.i.d. samples, each of size 100, where each draw is the number roll of a fair dice (number could be 1,2,3,4,5, or 6 with equal probability). This is essentially a 2-step process involving drawing from a uniform [0,1] and then converting the draw to the roll of a dice.

   • I plot the approximate sampling distributions of the first, forty-ninth and ninety-ninth elements of the sample: smoothed version of discrete pdf from roll of a fair dice.

   • I also plot the approximate sampling distribution of the sample mean: close to the normal pdf centered at 3.5 and with a variance of (2.9167/100). This demonstrates the Central Limit Theorem by showing that even when the population from which the random sample is being drawn is non-normal (roll of a dice in this example), the sample mean follows an approximate normal distribution. 

This entry captures one of the core concepts in Econometrics, namely, that of sampling distributions and what the CLT has to say about it. By itself, it can hold the fort, but I hope to populate the page as time goes by.

If you executed the .do file and benefitted from it, please drop me a line and let me know. If you have suggestions for other fun stuff, let me know too. email: dgoel.india@gmail.com or deepti_goel@pitzer.edu