48. Suppose that events occur according to a nonhomogeneous Poisson process with intensity function A(f), t > 0. Suppose that, independently of anything that has previously occurred, an event at time s will be counted with probability p(s), s > 0. Let Nc(t) denote the number of counted events by time t.

(a) What type of process if [Nc(t), t > 0J?

(b) Prove your answer to part (a).