Suppose that X₁,.......,X_n is a random sample from a gamma distribution with parameters.

Suppose that X1, . . . ,Xn is a random sample from a gamma distribution with parameters a = 3 and 5. (a) Find the maximum likelihood estimator, B, of 5 and show that it is unbiased. (b) Use moment generating functions to show that B is a consistent estimator of [3. (c) Find the variance of B and show that it achieves the RaoiCramr lower bound for unbiased estimators of [3