Consider a random sample of size n from a gamma distribution, X, GAM(0, K), and let X = (1/n) [X, and X = (X)/ be the sample mean and geometric mean, respectively (a) Show that X and X are jointly complete and sufficient for 8 and K. (b) Find the UMVUE of μ = 0K. (c) Find the UMVUE of μ". (d) Show that the distribution of T = X/X does not depend on 0. (e) Show that X and T are stochastically independent random variables. () Show that the conditional pdf of X given X = x does not depend on K.

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