Suppose that X1, . . . , Xn form a random sample from an exponential distribution for which the value of the parameter β is unknown (β > 0) and must be estimated by using the squared error loss function. Let δ be the estimator such that δ(X1, . . . , Xn) = 3 for all possible values of X1, . . . , Xn.
a. Determine the value of the M.S.E. R(β, δ) for β > 0.
b. Explain why the estimator δ must be admissible.