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Unformatted text preview: STAT/MA 416 October 24, 2011 Problem Set 24 Name: 1. Consider a pair of random variables X,Y with constant joint density on the triangle with vertices at (0 , 0), (3 , 0), and (0 , 3). a. For 0 y 3, find the conditional density f X  Y ( x  y ) of X , given Y = y . b. Find the conditional probability that X 1, given Y = 1. I.e., find P ( X 1  Y = 1). c. Find the conditional probability that X 1, given Y 1. I.e., find P ( X 1  Y 1). 1 2. Consider a pair of random variables X,Y with constant joint density on the quadrilateral with vertices (0 , 0), (2 , 0), (2 , 6), (0 , 12). a. For 0 y 6, find the conditional density f X  Y ( x  y ) of X , given Y = y . b. For 6 y 12, find the conditional density f X  Y ( x  y ) of X , given Y = y . c. Find the conditional probability that X 1, given 3 Y 9. I.e., find P ( X 1  3 Y 9)....
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 Fall '08
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 Probability

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