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Unformatted text preview: Stat 5101 (Geyer) Fall 2011 Homework Assignment 6 Due Wednesday, October 26, 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. 61. Suppose ( X,Y ) is a continuous random vector having PDF f. Say for each of the following definitions of f whether X and Y are independent or not. (a) f ( x,y ) = 4 xy , 0 < x < 1, 0 < y < 1. (b) f ( x,y ) = 8 xy , 0 < x < y < 1. (c) f ( x,y ) = 144( x 1 / 2) 2 ( y 1 / 2) 2 , 0 < x < 1, 0 < y < 1. (d) f ( x,y ) = 288( x 1 / 2) 2 ( y 1 / 2) 2 , 0 < x < y < 1. 62. Suppose X is a continuous random variable having PDF f ( x ) = 1 + x, 1 ≤ x < 1 x, ≤ x ≤ 1 , otherwise (a) Find E ( X ). (b) Find E ( X 2 ). (c) Find var( X 2 ). Hint: Since the PDF has a casesplitting formula, you must split integrals into pieces E { g ( X ) } = Z 1 g ( x ) f ( x ) dx + Z 1 g ( x ) f ( x )...
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 Spring '11
 Staff
 Probability distribution, Probability theory, probability density function, continuous random vector

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