# expected value

• January 26th 2009, 06:03 AM
BrainMan
expected value
How do I prove the following:

Let X and Y be discrete random variables. Show that
E[(X^2)Y given X] = (X^2)E[Y given X]

Thanks for any help.
• January 26th 2009, 10:54 PM
Constatine11
Quote:

Originally Posted by BrainMan
How do I prove the following:

Let X and Y be discrete random variables. Show that
E[(X^2)Y given X] = (X^2)E[Y given X]

Thanks for any help.

$E(X^2Y|X=x)=\int x^2y\ p(x,y) \ dy=x^2 \int y\ p(x,y) \ dy$

and:

$
E(Y|X=x)=\int y\ p(x,y)\ dy
$

.