Assignment 6

# Assignment 6 - Stat 5101 (Geyer) Fall 2009 Homework...

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Stat 5101 (Geyer) Fall 2009 Homework Assignment 6 Due Wednesday, October 28, 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. 6-1. 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. 6-2. Suppose X is a continuous random variable having PDF f ( x ) = 1 + x, - 1 x < 0 1 - x, 0 x 1 0 , otherwise (a) Find E ( X ). (b) Find E ( X 2 ). (c) Find var( X 2 ). Hint: Since the PDF has a case-splitting formula, you must split integrals into pieces E { g ( X ) } = Z 0 - 1 g ( x ) f ( x ) dx + Z 1 0 g ( x ) f ( x ) dx such that the PDF is deﬁned by one formula for each piece.

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## This note was uploaded on 10/28/2010 for the course STAT 5101 taught by Professor Staff during the Fall '02 term at Minnesota.

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Assignment 6 - Stat 5101 (Geyer) Fall 2009 Homework...

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