Consider a population in which each individual independently gives

birth at an exponential rate and dies at an exponential rate . In

addition, new members enter the population in accordance with a

Poisson process with rate . Let X(t) denote the population size at

time t.

(a) What type of process is {X(t), t 0}?

(b) What are its parameters?

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