I am working on a problem and am a little bit confused.
The problem:
P(X=0,Y=0) = .80
P(X=1,Y=0) = .05
P(X=0,Y=1) = .025
P(X=1,Y=1) = .125
Find Var(Y|X=1)
What I have done so far: (using)
E(Y$^2$|X=1) - $\big($E(Y|X=1)$\big)$$^2$
But with this I have been getting:
E(Y|X=1) = $(0)(.05) + (1)(.125)\over(.05+.125)$ = .71
and
E(Y$^2$|X=1) = $(0)^2(.05) + (1)^2(.125)\over(.05+.125)$ = .71
But with this we get the same answer so that when we do E(X$^2$) - (EX)$^2$
We get:
.71 - .71 = 0
This doesn't seem like it is the right answer to me? It seems like there would be some variation from Y | X = 1
Your approach is correct; but when you plug into $$ E(Y^2|X=1) - (E(Y|X=1))^2 $$ you still need to square the rightmost term.