Explanation on minimization of Expected values

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cutesteph
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Why is the E[ Y - f(x) ]^2 minimized when choosing f(x) = E[Y|X] ?
 
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Hye cutesteph.

Try finding when the expression is zero. Also since you are using two variables, what is the expectation with respect to?

Another thing to note is that E_y[E_x[Y|X]] = E[Y] (also known as conditional expectation).
 

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