Assignment 9

# Assignment 9 - Stat 5101(Geyer Fall 2009 Homework...

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Stat 5101 (Geyer) Fall 2009 Homework Assignment 9 Due Wednesday, November 25, 2009 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. Parts (e) and (f) of problem 8-9 deferred from the preceding home- work, which see for the problem statement. 9-2. Part (c) of problem 8-10 deferred from the preceding homework, which see for the problem statement. 9-3. Suppose E ( Y | X ) = X var( Y | X ) = 3 X 2 and suppose the marginal distribution of X is N ( μ,σ 2 ). (a) Find E ( Y ). (b) Find var( Y ). 9-4. Suppose X 1 , ... , X N are IID having mean μ and variance σ 2 where N is a Poi( λ ) random variable independent of all of the X i . Let Y = N X i =1 X i , with the convention that N = 0 implies Y = 0. (a) Find E ( Y ). (b) Find var( Y ). 9-5. Suppose that the conditional distribution of Y given X is Poi( X ), and suppose that the marginal distribution of

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Assignment 9 - Stat 5101(Geyer Fall 2009 Homework...

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