(a) If Y ~ T(a, A) with a 2 1, show that E(1/Y ) = 1/ (a - 1) for a > 1, and is infinite for a = 1 (you may find it useful to know that I(0) is infinite). (b) Let X1,. . ., X,, be independent random variables, each distributed as Exp()). Noting that E(X.) = And, two alternative estimators of A are proposed: n A1 = and n X, 12 - Sn where Sn = EL-1 Xi. i. State the distribution of S,. ii. Find the bias of each estimator. On this basis, which would you prefer? Do you need to consider anything else to determine which estimator is better overall? iii. 12 is biased. How would you modify it to obtain an unbiased estimator