Problem A4.2 -1 Let X be one observation from a population with beta(0, 1) PDF. That is, fx(x) = 0x01 for 0 x 1, and zero otherwise. a) For testing Ho: 0 1 against H: 0 > 1, find the size of the test that reject H if X > 0.9. b) Find the most powerful size a test of Ho: 0 = 1 against H: 0 = 3. c) Is there a UMP test of size a for testing Ho: 0 1 against H: 0 > 1? If so, find it. If not, prove so.