** URGENT **

Sampling Distribution - WorkShop 18

PYTHON

All the parts are of just one question and can only be implemented combinedly so please answer all of the parts. I cannot post them separately because of that reason. I will 100% upvote if you do that, I promise.

Illustrate the Law of Large Numbers and the Central Limit Theorem for the t,-distribution for different values of v. Write a Python notebook for the following simulation for a given value of v. Start with v= 100. = = ...) (a) Draw M i.i.d. random samples of length N from the t, distribution. Start with M = 500 and N = 10,000 but you should experiment with different values. (b) For each sample m = 1, M, compute the sample means for the first n= - 5, 10, 100, 500, 1000, 10000 draws of the sample. (c) For each n, compute the mean, standard deviation and variance of the sample means across the M samples. This yields means, standard deviations, and variances for each of the six different values of n. Report your results in a table. (d) For each n, plot the distributions of the M sample means. (e) Describe how these simulations relate to the LLN and the CLT. Be careful to distin- guish the implications of the LLN and the CLT. (f) Repeat steps (a) to (e) for v = 10,5, 2, 1,0.5