Problem 4. Let X1,..., Xn be iid copies of a random variable X ~ N(0, o?), where o > 0. (a) [8 points] Show that E(XD) = ov and Var(|XI) = (1 - 2) 2. Use these results to construct a method of moments estimator on for o, which is a linear function of |X]| . . . |Xml- (b) [8 points] Using the Central Limit Theorem or otherwise, compute the lim- iting distribution, as n -+ co, of Vn(on - 0). (c) [9 points] Another method of moments estimator is given by On := X ?. n 1=1 Once again using the Central Limit Theorem (CLT) or otherwise, compute the limiting distribution, as n -+ oo, of vn(on - a). You do not need to justify the use of the CLT as part of your answer. Recall that the asymptotic relative efficiency (ARE) of two estimators (6, )nEN and (67)nEN is given by ARE(6, 8)= Var(6!) Var (62) and we say that o, is relatively more efficient if ARE(6, 6,) > 1. Using this concept, compare the efficiency of on and on