(adsbygoogle = window.adsbygoogle || []).push({}); need urgent help with a conditional variance proof.

I have been given this problem and I'm pretty stumped.

I want to prove that Y=g(X) if and only if var(YlX) = 0.

so if var(YlX)=0 then

E(Y^2lX) - E(YlX)^2 = 0

E(Y^2lX) =E(YlX)^2

so what should I do now? I tried showing that this equation is true when y =g(X), but in the end I end up with var(g(X)) = 0...unless I did something wrong.

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# Need help with a conditional variance proof.

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