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assign07

# assign07 - X and E X the expected value of X 2 Suppose that...

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Math 302.102 Fall 2010 Assignment #7 This assignment is due at the beginning of class on Monday, November 22, 2010. 1. Let 0 < a < b be given positive constants, and suppose that the random vector ( X,Y ) has joint density function f X,Y ( x,y ) = ( c ( y - x ) , if a < x < y < b, 0 , otherwise , where the value of the normalizing constant c is chosen so that Z -∞ Z -∞ f X,Y ( x,y ) d x d y = 1. (a) Determine the value of c . (Of course, your answer will depend on a and b .) (b) Determine f Y ( y ), the marginal density function of Y , and E ( Y ), the expected value of Y . (c) Determine f X ( x ), the marginal density function of
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Unformatted text preview: X , and E ( X ), the expected value of X . 2. Suppose that the random vector ( X,Y ) is jointly distributed with joint density function f X,Y ( x,y ) = ( 2 e-x-y , if 0 &amp;lt; x &amp;lt; y &amp;lt; , , otherwise . (a) Determine the marginal density functions f X ( x ) and f Y ( y ). (b) Based on your answer to (a) , are X and Y independent random variables? Justify your answer. (c) Use the result of (a) to calculate E ( X ) and E ( Y )....
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