48. Suppose that we want to predict the value of a random variable X by using one...
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48. Suppose that we want to predict the value of a random variable X by using one of the predictors Y1, . . . , Yn, each of which satisfies E[Yi |X] = X. Show that the predictor Yi that minimizes E[(Yi − X)2] is the one whose variance is smallest.
Hint: Compute Var(Yi) by using the conditional variance formula.
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