Suppose A is one observation from a population with beta(0,1) pdf.
(a) For testing H0: θ ≤ 1 versus H1: θ > 1, find the size and sketch the power function of the test that rejects H0 if X > 1/2
(b) Find the most powerful level α test of H0: θ = 1 versus H1: θ = 2.
(c) Is there a UMP test of H0: θ ≤ 1 versus H1: θ > 1? If so, find it. If not, prove so.