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Unformatted text preview: ( x ) , the ratio of the joint pdf of X and Y and the marginal pdf of X . Conditional expectation and conditional variance Conditional expectation E ( X  Y = y ) is the expectation with respect to the conditional distribution: E ( X  Y = y ) = Z ∞∞ xf X  Y ( x  y ) dx. Conditional variance Var( X  Y = y ) is the variance with respect to the conditional distribution: Var( X  Y = y ) = E ( X 2  Y = y )( E ( X  Y = y )) 2 where E ( X 2  Y = y ) = Z ∞∞ x 2 f X  Y ( x  y ) dx. Example : Let ( X,Y ) be a continuous random vector with a joint pdf f X,Y ( x,y ) = 15 xy 2 , ≤ x,y ≤ 1 ,y ≤ x. • Compute the conditional densities f X  Y and f Y  X ; • Compute the conditional mean and the conditional variance of Y given X = x for < x < 1....
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 Fall '10
 SAMORODNITSKY
 Probability theory, conditional pmf, conditional variance var

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