Question: Question 3 (20 marks) a). Let X, be iid, E(X) = and Var(X) = o. Set X = Xi/n. Show that i=1 n (X-X)

Question 3 (20 marks) a). Let X, be iid, E(X) = and

Question 3 (20 marks) a). Let X, be iid, E(X) = and Var(X) = o. Set X = Xi/n. Show that i=1 n (X-X) 0 n i=1 (10 marks) b). Suppose X, x 1 are independent random variables and suppose that X, has a gamma density fk (x) fk (x) = -,x>0, yk>0 () Give necessary and sufficient conditions for E-1 X to converge almost surely. (10 marks)

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