Xn) from the Consider a random sample X: px n = (x1, X2, multivariate normal distribution, where the column vectors x; (of X) are independently and identically distributed as N(, ). Let 1/1X; and S X = i (x - x)(x - x)' - n n-I a. Show that the sample mean (x) and the sample covariance matrix (S) are unbiased estimators of u and b. Show that x ~ N (1, 8) c. Show (n 1)S is distributed as the Wishart random variable with parameters n 1 and , that is (n 1)S ~ W(n 1, ) d. Let W W(n, E). Show that E[W] = n.