Unformatted text preview: f ( x | y ) = f ( x, y ) /f ( y ) is the conditional p.d.f. of X given Y . • If X is discrete and Y is continuous, then we formally write E ( X ) = ² E ( X | Y = y ) f ( y ) dy and evaluate the integral by applying properties 1., 3., 4. in conjunction with any known conditional information. In particular, if X = I A (an indicator variable) then E ( I A | Y = y ) = P ( A | Y = y ) and so P ( A ) = E ( I A ) = ² P ( A | Y = y ) f ( y ) dy where the integral is evaluated using properties of conditional probability analogous to those of conditional expectation....
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- Spring '08
- Probability theory, Conditional expectation, aj E, conditional information