Suppose that a stock is currently worth $64, and each month its value either goes up by 25% (with probability 2/3) or goes down by 25% (with probability 1/3), with the stock's behavior in successive months assumed independent. (a) Find the different values of the random variable X, defined by X = S3- min{So, S1, S2, S3}. Then find E(X). (Hint. Note that X is defined on the state space of S3, which is {w*wtw+,wtw+w,wtw-w,wtwwt,wwtw,www*,w ww,www}. For example, we have X (wtwtw) = Sa (wtwtw) min{So, Si(w+), S2(wtw+), Sa(wtw+w)}.) (b) then use the fact that E(XY) = E(X)E(Y) if X and Y are independent random variables.) Find E(S20). (Hint. Write S20 as a multiplication of total returns and