Question 3 (20 marks) a). Let X, be iid, E(X) = and Var(X) = o....
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Question 3 (20 marks) a). Let X, be iid, E(X) = μ and Var(X) = o². Set X = Xi/n. Show that i=1 n ¹Σ(X₁-X) ² ² 0²² 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 Γ(γκ) Give necessary and sufficient conditions for E-1 X to converge almost surely. (10 marks) Question 3 (20 marks) a). Let X, be iid, E(X) = μ and Var(X) = o². Set X = Xi/n. Show that i=1 n ¹Σ(X₁-X) ² ² 0²² 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 Γ(γκ) Give necessary and sufficient conditions for E-1 X to converge almost surely. (10 marks)
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a Lets prove the given equation X Xin where i goes from 1 to n To simplify the equation l... View the full answer
Related Book For
Probability And Statistics
ISBN: 9780321500465
4th Edition
Authors: Morris H. DeGroot, Mark J. Schervish
Posted Date:
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