*** Please answer the following question and the Matlab codings

2. (30 pts) Central Limit Theorem Let X1,X2,... be a sequence of iid random variable with finite mean / and finite variance o', and let Mn be the mean of the first n random variables in the sequence: Mn = X1+ X2+ ...+ Xn n (a) Let X; be a uniform continuous random variable taking values in the interval (2, 6). Write a MATLAB program to plot the pdf and cdf of Mn. Consider n = 1, 2, 3, 4, 5, 10, 20, 30 and compare your results.(b) Calculate analytically the mean and the variance of Xi and of Mn in part (a). (0) Write a MATLAB program to generate a multivariate Gaussian random variable with the same mean and variance as M\". Superimpose this plot on the plots from part (a). (d) Repeat parts (a), (b), and (c) with X;- representing a toss of an unfair 5-sided die with each even side ({2, 4}) twice as likely as each odd side ({1, 3, 5}). Use t = 104 samples in the above. While plotting histogram for discrete data, use t - - 1 B1nW1dth' as n+1'