2. Let S(t) denote the price of a security at time. A population model for the process {S(t), t 2 0} supposes that the price remains changed until a "shock" occurs, at which time the price is multiplied by a random factor. If we led(t) denote the number of shocks by timet, and let X, denote the ith multiplicative factor, then this model supposes that N(t) S(t) = S(0) II Xi where i=1 N(t) X; is equal to 1 whenN(t) = 0. Suppose that they; are independent exponential random variables with rate/; that {NV(t), t 2 0} is a Poisson process with rate ; that {N(t), t2 0} is independent of the X,; and that S(0) = s. (a) Find ES(t) }. (b) Find ES(t) 2}