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Unformatted text preview: Stat 5101 (Geyer) Fall 2011 Homework Assignment 4 Due Wednesday, October 5, 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. 41. If U , V , X , and Y are any random variables, show that cov( U + V,X + Y ) = cov( U,X ) + cov( V,X ) + cov( U,Y ) + cov( V,Y ) 42. Suppose X 1 , X 2 , X 3 are IID with mean μ and variance σ 2 . Calculate the mean vector and variance matrix of the random vector Y = Y 1 Y 2 Y 3 = X 1 X 2 X 2 X 3 X 3 X 1 43. Suppose X and Y are independent random variables, with means μ X and μ Y , respectively, and variances σ 2 X and σ 2 Y , respectively. Calculate E ( X 2 Y 2 ) in terms of μ X , μ Y , σ 2 X , and σ 2 Y . 44. Suppose 6 balls that are indistinguishable except for color are placed in an urn and suppose 3 balls are red and 3 are white. Suppose 2 balls arein an urn and suppose 3 balls are red and 3 are white....
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This note was uploaded on 09/13/2011 for the course STA 4184 taught by Professor Staff during the Spring '11 term at University of Central Florida.
 Spring '11
 Staff

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