2. (Expected Value/Utility) Suppose that your utility function is () = , and that you are offered a gamble which allows you to win $25 if you are lucky and $9 if you are not. Suppose that the probability of winning $25 is 1/3 and the probability of winning $9 is 2/3 .

a) What is the expected value of this gamble?

b) What is the expected utility of this gamble?

c) What is the certainty equivalent of the gamble; that is, what is the amount of money X such that you are indifferent between receiving $X for sure and playing the gamble?

d) Imagine now that the probability of winning $25 is and the probability of winning $9 is 1 . If the expected utility of the gamble equals 4, what is ?