4. Pancreatic cancer takes one of three types, say with probabilities p1 = .25, p2 = .50 and p3 = .25. Let J indicate the type. Suppose that the patient's lifetime T, given J = j, has exponential(j;5') conditional distribution, j = 1, 2, 3. (a) Use iterated expectations to nd E(T). (1)) Use the partition formula for variance to nd Var(T). (c) Now express the pdf for T as a mixture, Ht) 2 $6413 + get/cm + %,3t/(2:5)a t > 0} and compute the mean and variance by direct integration