Suppose that we want to predict the value of a random variable X by using one of

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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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Introduction To Probability Models

ISBN: 9780443187612

13th Edition

Authors: Sheldon M. Ross

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Question Posted: Sep 05, 2024 07:04 AM

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Suppose that we want to predict the value of a random variable X by using one of

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Introduction To Probability Models

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