Question: Suppose that a persons utility function is U(x) = x2 for x 0. Show that the person will always prefer to take a gamble

Suppose that a person’s utility function is U(x) = x2 for x ≥ 0. Show that the person will always prefer to take a gamble in which she will receive a random gain of X dollars rather than receive the amount E(X) with certainty, where Pr(X ≥ 0) = 1 and E(X) < ∞.

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