A decision maker has utility function u(x) = ?x with x ? 0. He is given the choice between two random amounts X and Y, in exchange for his entire present capital ?. The probability distributions of X and Y are given by

(a) Show that he prefers X to Y.

(b) Determine for which values of ? he should decline the offer.

(c) Propose an utility function with which he would prefer Y?to X.

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400 900 Pr[X = x] 0.5 0.5 and 100 1600 Pr[Y = y] 0.6 0.4 400 900 Pr[X = x] 0.5 0.5 and 100 1600 Pr[Y = y] 0.6 0.4