Let Y be a random variable that we would like to predict Suppose that we must choose a single number d as the prediction and that we will lose (Y d)2 dollars Suppose that our utility for dollars is a square root function Prove that the value of d that maximizes expected utility is a median of the distribution of Y if x20, U(x) x if x 0

Question: Let Y be a random variable that we would like to predict. Suppose that we must choose a single number d as the prediction and

Let Y be a random variable that we would like to predict. Suppose that we must choose a single number d as the prediction and that we will lose (Y ˆ’ d)2 dollars. Suppose that our utility for dollars is a square root function:

Prove that the value of d that maximizes expected utility is a median of the distribution of Y.

if x20, U(x) = -x if x

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