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I'm trying to understand my teacher's proof. He starts by showing that the c that minimizes $E((Y-c)^2))$ is $E(Y)$, which I understand.

But then he says that $E((Y-g(X))^2) \geq E((Y-E(Y|X)^2)$, as if that was obvious from the previous result. How can you go from one to the other?

Thanks!

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