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Unformatted text preview: c. {X 2 < Y}. 7. Let X and Y be independent random variables with Y uniformly distributed from 0 to 1. Let X have cdf and pdf F X ( x ) and f X ( x ), respectively. Show that the pdf of the random variable Z = X + Y is given by ) 1 ( F ) ( F ) ( f X X Z= z z z 8. The joint density function of X and Y is given by & > > = +otherwise , ) , ( f ) ( y x e y x y x XY Find the density function of the random variable X/Y 9. Two fair dice are rolled. Find the joint probability mass function of X and Y when a. X is the larger value rolled and Y is the sum of the two values. b. X is the smaller and Y is the larger value rolled....
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 Fall '08
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