Consider again the conditions of Exercise 2. Let Yn = max{X1, . . . , Xn} and consider the estimator 2(X1, . . . ,Xn)

Consider again the conditions of Exercise 2. Let Yn = max{X1, . . . , Xn} and consider the estimator δ2(X1, . . . ,Xn) = Yn.
a. Determine the M.S.E. R(θ, δ2) for θ >0.
b. Show that for n = 2, R(θ, δ2) = R(θ, δ1) for θ >0.
c. Show that for n ≥ 3, the estimator δ2 dominates the estimator δ1.