# Math Help - The conditional properties of 2 exponential functions

1. ## 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

Why is it obvious that $E(X|Y)=Y$ and $Var(X|Y)=Y^2$ ??

2. 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...