Consider a population in which each individual independently gives birth at an exponential rate A and dies at an exponential rate In addition, new members enter the population in accordance with a Pois- son process with rate 0 Let X(t) denote the population size at time t.

(a) What type of process is {X(1), 1 0}"

(b) What are its parameters?

(c) Find E[X(t)|X(0) = i]