2. Suppose that Y1, ..., Y, is a sample of size n from a Beta(0, 1), with pdf f(y; 0) = 0y-1, 0 >0, 0 0). [Hint: - In Y; ~ Exp(1/0)] (b) Derive the uniformly most powerful test for testing Ho : 0 = do versus Ha : 0 > do at the significance level a. (c) Find the ML estimator 0 of 0. (d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided 1 - a CI for e