09_19 - b) Find the marginal probability mass function for...

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STAT 410 Examples for 09/19/2008 Fall 2008 1. Let X and Y have the joint p.d.f. f X Y ( x , y ) = 20 x 2 y 3 , 0 < x < 1, 0 < y < x . a) Find f X ( x ), f Y ( y ). b) Find f X | Y ( x | y ), f Y | X ( y | x ). c) Find E ( X | Y = y ), E ( Y | X = x ). d) Find E ( X ), E ( Y ). 2. Let λ > 0. Consider the following joint probability distribution p ( x , y ) of two random variables X and Y: p ( x , y ) = ( ) ! 1 + - x e x , x , y – integers, 0 y x . a) Verify that p ( x , y ) is a legitimate probability mass function.
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Unformatted text preview: b) Find the marginal probability mass function for X. c) Find the marginal probability mass function for Y. d) Find E ( Y ), E ( X Y ). e) Find the moment-generating function M ( t 1 , t 2 ). f) Find the conditional probability distribution p Y | X ( y | x ) of Y given X = x . g) Find conditional expectation E ( Y | X ) and use it to find E ( Y )....
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