Let X1, . . . , Xn be iid from an exponential family distribution with k = 1: f(x | ) = a()b(x)e^c()d(x) . We wish to find the UMP size- test for the hypotheses H0 : = 0 vs H1 : = 1 (0

(a) Prove that if the function c() is increasing in , then the UMP test has form R = {T > c} where T = Sumation d(Xi).

(b) Determine the form of the rejection region if 0 > 1 and c() is an increasing function; if 0