Yuki has a utility function given by u(x) = ln(x). She faces a gamble that pays 10 with probability .5 and 15 with probability .5. (a) What is the expected value of this gamble? (b) What is Yuki's certainty equivalent xCE - that is, what sure amount must he receive in order to be indifferent between the gamble and this sure amount? (c) Find xCE if Yuki's utility was given by U(x) = x (d) Find xCE if Yuki's utility was given by U(x) = x 2 . (e) Comment on how Yuki's certainty equivalent relative to the expected value varies as her utility function goes from concave from convex