1.6. Operations 1, 2, and 3 are to be performed in succession on a major piece of equipment. Operation k takes a random duration Sk that is exponentially distributed with parameter Ak for k = 1, 2, 3, and all operation times are independent. Let X(t) denote the operation being performed at time t, with time t = 0 marking the start of the first operation. Suppose that A, = 5, A, = 3, and A, = 13. Determine

(a) P,(t) = Pr{X(t) = 1).

(b) P,(t) = Pr{X(t) = 2).

(c) P,(t) = Pr{X(t) = 3}.