Question: 2. Suppose X1, X2, - - - , X constitute a random sample from a population following a N (y, 9) distribution, where the mean

2. Suppose X1, X2, - - - , X\" constitute a random sample from a population following a N (y, 9) distribution, where the mean p is known and the variance 9 > 0 is unknown. (X; m2? (a) What is the distribution of (b) Use the result from (a), show that Var(X12) = 262 + 4p26. You may use the fact that E(Xi3) = p3 + 3p6. 1 n (c) Show that T1 = E Z X? p2 is a moment estimator of 6 by considering the i=1 second raw moment of X. 1 n (d) It is known that T; = Z (X,- p)2 is the maximum likelihood estimator of n i=1 6. Which estimator is unbiased? T1, T2 or both? (e) Are T1 and T2 consistent estimators? (f) Find Eff(T1, T2). Which estimator is more elcient

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