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# Quiz2Bans - 15 8 10 2 1 15 10 4 3 = =-x x = 0.3125 b(6 Find...

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STAT 410 Spring 2008 Version B Name ANSWERS . Quiz 2 (10 points) Be sure to show all your work, your partial credit might depend on it. No credit will be given without supporting work. 1. Let X and Y have the joint probability density function f ( x , y ) = ° ° ± ° ° ² ³ < + > > otherwise 0 1 , 0 , 0 60 2 y x y x y x a) (4) Find P ( X < Y ) . P ( X < Y ) = ´ ´ µ µ · ¸ ¸ ¹ º - 2 1 0 1 2 60 dx dy y x x x = ´ ´ µ µ · ¸ ¸ ¹ º - 2 1 0 1 2 2 30 dx dy y x x x = ( ) ( ) ´ - - 2 1 0 2 2 2 1 30 dx x x x = ( ) ´ - 2 1 0 2 2 1 30 dx x x = ( ) ´ - 2 1 0 3 2 60 30 dx x x = ( ) 16 5 16 15 8 10 0 2 1 15 10 4
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Unformatted text preview: 15 8 10 2 1 15 10 4 3 = =--x x = 0.3125. b) (6) Find E ( Y | X = x ). f X ( x ) = ´-x dy y x 1 2 60 = ´-x dy y x 1 2 2 30 = ( ) 2 2 1 30 x x-, 0 < x < 1. f Y | X ( y | x ) = ( ) ( ) x f y x f , X = ( ) 2 2 2 1 30 60 x x y x-= ( ) 2 1 2 x y-, 0 < y < 1 – x . E ( Y | X = x ) = ( ) ´--⋅ x dy x y y 1 2 1 2 = ( ) ´-⋅-x dy y x 1 2 2 1 2 = ( ) 1 3 2 x-⋅ , 0 < x < 1....
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