please focus on e and f

iid 4. Let X1, ... , Xn 120 N(0,02), - 0. Assume 02 is known. Denote Za as the 100(1 a)-th percentile of the standard normal distribution. (a) Find the maximum likelihood estimator for 0. (b) Show that a most powerful critical region of size a = 0.05 for testing Ho : 0 = 1 versus Hp : 0 = 2 is {(x1, ... , X16): 4 1)/0 > 1.645}. (c) Write down the power function r(e) for the hypothesis test (b). (d) Show that y(2) = 0.991 if o2 = 1. (e) Find a Uniformly Most Powerful critical region of size a = 0.05 for testing Ho : 0 = 1 versus H1:0 > 1 (f) Is there a Uniformly Most Powerful critical region for testing Ho : 0 1 ? Why or why not