Math 193a, HANDOUT FOR HOMEWORK Some Answers and Solutions

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39. This exercise is a generalization of Exercise 38. Let u be a utility function, a r.v. X1 has the original distribution, and X2 has the transformed distribution. Then E{u(X1)} = ∑k u(xk)pk. The corresponding representation E{u(X2)} is the same except the terms with k = i−1, i, and i+1. Consequently, the difference E{u(X1)}−E{u(X2)}=−∆u(xi−1)+2∆u(xi)−∆u(xi+1) = 2∆ [ u(xi)− 1 2 (u(xi−1)+u(xi+1)) ] .

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تاریخ انتشار 2017