Let 8(t) denote the price of a security at time t. 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 let N (t) denote the number of shocks by time t, and let X; denote the ith multiplicative factor, then this model supposes that where Hi3? X2- is equal to 1 when N (t) = 0. Suppose that the Xi are independent exponential random variables with rate ,u; that {N (t),t 2 0} is a Poisson process with rate A; that {N(t),t 2 0} is independent of the X2; and that 8(0) = s. (a) Find E{S(t)}. (b) Find E{S(t)2}