Problem 5: Suppose we have k (k 2 2) independent samples. For each i = 1, . .., k, the i-th sample is of size n; and for j = 1, ..., n, Xij are i.i.d. N(pi, 62) with o unknown. We want to test Ho : #1 = /2 = . . . = Ax against H1 : A; are not all equal. Use Wilks' Theo- rem to derive the critical region of the generalized likelihood test at the significance level a