*36. Let denote the price of a security at time t. A popular model for the process supposes that the price remains unchanged until a “shock” occurs, at which time the price is multiplied by a random factor. If we letI mage denote the number of shocks by time t, and let denote the ith multiplicative factor, then this model supposes that where is equal to 1 whenI mage. Suppose that the are independent exponential random variables with rate μ; thatI mage is a Poisson process with rate λ; thatI mage is independent of the ;
and that .

(a) Find .

(b) Find .