Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

Please help!!

EDIT: GOT IT, nevermind :)

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- Sep 17th 2011, 06:14 PMAzaleaSuppose E[Y|X]=1. Show Cov(Y,X)=0.?
Suppose E[Y|X]=1. Show Cov(Y,X)=0.?

Please help!!

EDIT: GOT IT, nevermind :) - Sep 18th 2011, 03:03 AMSpringFan25Re: Suppose E[Y|X]=1. Show Cov(Y,X)=0.?
just for fun, since the OP has the answer anyway:

first:

$\displaystyle E(Y) = E_xE(Y|X) = E_x(1) = 1$

and

$\displaystyle E(XY)=E_x(E(XY|X)) = E_x(E(X|X)E(Y|X)) = E_x(X \cdot 1)$

$\displaystyle = \sum x P(X=x)$

$\displaystyle = E(X)$

Then

$\displaystyle Cov(X,Y) = E(XY) - E(Y)E(X) = E(X) - 1 \cdot E(X) = 0$