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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. 4-1. 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 ) 4-2. Suppose X 1 , X 2 , X 3 are IID with mean and variance 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 4-3. Suppose X and Y are independent random variables, with means X and Y , respectively, and variances 2 X and 2 Y , respectively. Calculate E ( X 2 Y 2 ) in terms of X , Y , 2 X , and 2 Y . 4-4. 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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- Spring '11