Suppose that we have a random sample of four observations from the density function f (y | θ) =    1 2θ 3 y2 e−y/θ , y > 0, 0, elsewhere. A. Find the rejection region for the most powerful test of H0 : θ = θ0 against Ha : θ = θa , assuming that θa > θ0.
B. Is the test given in part (a) uniformly most powerful for the alternative θ > θ0?