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# h9 - Stat 5102(Geyer Spring 2012 Homework Assignment 9 Due...

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Stat 5102 (Geyer) Spring 2012 Homework Assignment 9 Due Wednesday, April 11, 2012 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. 9-1. Suppose X is Bin( n, p ) and the prior distribution for p is flat (a proper prior, since p is bounded). (a) Find the posterior distribution for p . (b) Find the mean of the posterior distribution for p . (c) Find the standard deviation of the posterior distribution for p . (d) Find the mode of the posterior distribution for p . (e) In the case x = 0, n = 10, find the posterior median for p . 9-2. Suppose X 1 , . . . , X n are IID Exp( λ ) and the prior distribution for λ is flat (an improper prior). The posterior distribution for λ was found in problem 8-10 (a). (a) Find the mean of the posterior distribution for λ . (b) Find the standard deviation of the posterior distribution for λ .

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