Problem 2. "Multivariate Gaussian." Suppose we have N i.i.d. observations X = {xi}, from a multivariate Gaussian distribution xi lu ~ N ( u, Z) with unknown mean parameter u and a known covariance matrix E. As prior infor- mation on the mean parameter we have u~ N(mo, So). (a) Derive the posterior distribution p(y|X) of the mean parameter y. (b) Compare the Bayesian estimate (posterior mean) to the maximum likelihood es- timate by generating N = 10 observations from the bivariate Gaussian For this you can use the Python function numpy.random.normal , making use of the fact that the elements of the bivariate random vectors are independent. In the Bayesian case, use the prior with mo = [0, 0]' and So = o o.1]. [0.1 0 ]. Report both estimates. Is the Bayesian estimate closer to the true value y = [0, 0]T