Suppose E[Y|X]=1. Show Cov(Y,X)=0.?
Please help!!
EDIT: GOT IT, nevermind
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
$\displaystyle Cov(X,Y) = E(XY) - E(Y)E(X) = E(X) - 1 \cdot E(X) = 0$