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Math Help - conditional expectation and variance

  1. #1
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    conditional expectation and variance

    Let X, Y be independent exponential random variables with means 1 and 2 respectively.

    Let
    Z = 1, if X < Y
    Z = 0, otherwise

    Find E(X|Z) and V(X|Z).

    We should first find E(X|Z=z)
    E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
    However, how do we find f(x|z) ?
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  2. #2
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    Quote Originally Posted by allrighty View Post
    Let X, Y be independent exponential random variables with means 1 and 2 respectively.

    Let
    Z = 1, if X < Y
    Z = 0, otherwise

    Find E(X|Z) and V(X|Z).

    We should first find E(X|Z=z)
    E(X|Z=z) = integral (from 0 to inf) of xf(x|z).
    However, how do we find f(x|z) ?

    Bayes theorem:

    f(x|z)=\frac{p(z|x)f_X(x)}{p(z)}

    RonL
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