Problem 6 17 pts let a 7 points i let hint

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Unformatted text preview: he calculations in part c lead to convergence in distribution of ∑ √ via the generalized CLT. Problem 6 (17 pts). Let ∑ , a. (7 points) | (I) ∑ Let | Hint: Are the (I) represents. be random variables and denote . Prove: (I), where a {| |} | | | | events in (I) disjoint? Try to express in words what From now on assume that b. (6 points) Prove: (I) a| are independent. | c. (4 points) | If converge in probability then a probability as ∞. | | Hint: Prove first that Then combine parts a and b. Remark: It follows from part c that converge a.s. | | as | in ∞....
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This document was uploaded on 03/01/2014 for the course STATS 400 at Michigan State University.

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