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Math Help - The conditional properties of 2 exponential functions

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    The conditional properties of 2 exponential functions

    Suppose f_{X|Y}(x|y)=\frac{1}{y}e^{-\frac{x}{y}} and f_Y(y)=e^{-y} where 0<x,y<\infty

    Why is it obvious that E(X|Y)=Y and Var(X|Y)=Y^2 ??
    Last edited by noob mathematician; October 16th 2010 at 10:19 PM.
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    Hello,

    The distribution of X|Y is that of an exponential distribution with parameter 1/Y. So its expectation will be 1/(1/Y)=Y and the variance...
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