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Explanation on minimization of Expected values

  1. Nov 3, 2012 #1
    Why is the E[ Y - f(x) ]^2 minimized when choosing f(x) = E[Y|X] ?
     
  2. jcsd
  3. Nov 3, 2012 #2

    chiro

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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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