Let X1 and X2 be two independent and identically distributed random variables with N(u, 1) distribution. (a) Calculate a sufficient statistic for u. [5] (b) Suppose that we are interested in estimating the parameter 4 = 4 + 15 + 452. Find k such that = X9 - k is an unbiased estimator of p. [6] Hint: what is the sixth moment of the normal distribution? (c) Calculate the conditional distribution X1 | {X1 + X2 =s}. [10] (d) Use the Rao-Blackwell theorem to find an unbiased estimator of 4, denoting this estimator as , such that Var(4)