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Unformatted text preview: (b) Provide the conditional probability density function of X given Y = 0 : 7. [4 pts] (c) Provide P ( X > : 95 j Y = 0 : 7). [4 pts] 2. Suppose we have two random variables X and Y with joint probability density function f X;Y ( x;y ) = ( e x if 0 y x < 1 ; otherwise : (a) Provide P ( X < 2 ;Y > 1). [2 pts] (b) Provide P ( X 2 Y ). [4 pts] (c) Provide the marginal density fucntion of X . [4 pts] 3. Consider X and Y with joint density function as in Problem 1. (a) Provide E [ X ]. [2 pts] (b) Provide E [ X + Y ]. [4 pts] (c) Proivde V ( X + Y ). [4 pts] Hint: Note that E [ g ( X;Y )] = R 1 1 R 1 1 g ( x;y ) f X;Y ( x;y ) dxdy . 4. Let X and Y be independent random variables with E [ X ] = 56 ;V ( X ) = 16, and E [ Y ] = 5 ;V [ Y ] = 4. (a) Provide Cov ( X;Y ). [2 pts] (b) Provide V ( X + Y ). [4 pts] (c) Provide V ( X Y ). [4 pts]...
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 Spring '08
 Staff
 Probability

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