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2. Let X1, X2, . .. . X, be a random sample of size n from an Exp(1/0) distribution (i.e with mean 0 and variance 0?). (a) Derive an expression for E(X ) and Var(X ) in terms of 0 where X is the mean of the random sample. [3] (b) Express MSE(X) in terms of Var(X) and Bias?(X) and hence find an expression for MSE(X ) in terms of 0 . (c) Consider the family of estimators for 0 of the form Y = aX. Find MSE(aX ) and determine the value of a' such that Y* = a' X is the most efficient estimator of the form Y = aX