Let f:Z5→Z5 be a random permutation function. What is the probability Pr[ f(2) = 2| f(O) = O and f(1) = 1 ]? Express your answer as a reduced fraction without any spaces (eg, 1/10 and not 2/20 or 0.1), or as O or 1, if appropriate.

What values of a, b, c, and d should be used to calculate the probability shown below? xy OSxs1 1

Let Y be a discrete random variable with generating function 4 Gy (s) 6 – s s2 What is Var(Y) (in decimal)? Answer:

An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here