4. Let X be a k-dimensional isotropic Gaussian random variable with mean / and standard deviation o. Then the probability density function of X is a product of Gaussians in each of the coordinate directions, i .e. , k P(X = d) = II exp V2TO (-(d[i] - [2])2/202), i=1 which is same as P ( X = d) = (V2To) k exp(-Id - 1/2/202). (a) For k = 2, ji = (5, 4) and o = v3 generate 1000 samples of X and plot them. (2) (b) Given data D = {d1, d2, . .., dn} derive MLE estimates for ji and o2. (2) (c) Calculate MLE for ji and o for the sample of 1000 2-dimensional points generated in part (a). (2) (d) Now generate 1000 samples using the MLE estimates for ji and o and plot in the same figure as in part (a). You should use different colors for the two samples. (2)