Problem 1 A Gamma random variable Y has pdf JY(y:0. B) = [(0)83 e, 05y500 otherwise Here a > 0,8 > 0, E(Y) = of, and Var(Y) = of2. Suppose that we have a random sample of size n from a Gamma distribution. For the following parts (a) - (c) suppose that o = 2 is known. (a) We know that I'm is complete sufficient for B (when a is known). Find the UMVUE for B using the Lehmann-Scheffe Theorem. (b) Find the (Fisher) expected information of the sample. (c) Use the Cramer-Rao Lower Bound Method to verify that the estimator found in part (a) is the UMVUE of B (i.e. show that the variance of the estimator attains the CRLB). *Note that it is redundant to use CRLB method when the UMVUE has already been found using the Lehmann-Scheffe Theorem