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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 ex-pectation with respect to the conditional dis-tribution: E ( X | Y = y ) = Z ∞-∞ xf X | Y ( x | y ) dx. Conditional variance Var( X | Y = y ) is the vari-ance with respect to the conditional distribu-tion: 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 con-ditional variance of Y given X = x for < x < 1....

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- '10
- SAMORODNITSKY
- Probability theory, conditional pmf, conditional variance var