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hC - Stat 5101(Geyer Fall 2011 Homework Assignment 12 Due...

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Stat 5101 (Geyer) Fall 2011 Homework Assignment 12 Due Wednesday, December 14, 2011 Solve each problem. Explain your reasoning. No credit for answers with no explanation. If the problem is a proof, then you need words as well as formulas. Explain why your formulas follow one from another. 12-1. Give the details of the argument that the Poi( μ ) distribution is ap- proximately normal when μ is large. 12-2. Suppose X 1 , X 2 , ... are IID with mean μ and variance σ 2 and X n = 1 n n X i =1 X i What is the approximate normal distribution of sin( X n ) when n is large? 12-3. Suppose X 1 , X 2 , ... are IID Poi( μ ) random variables and X n = 1 n n X i =1 X i To what random variable does n ( e - X n - e - μ ) converge in distribution? 12-4. Suppose X 1 , X 2 , ... are IID Ber( p ) random variables with 0 < p < 1 and X n = 1 n n X i =1 X i (a) What is the approximate normal distribution of X n (1 - X n ) when n is large? (b) There is something unusual about the case

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hC - Stat 5101(Geyer Fall 2011 Homework Assignment 12 Due...

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