(Death Process with Immigration) Consider a population of size n, n ≥ 0, of a certain species in which individuals do not reproduce. However, new individuals immigrate into the population at a Poisson...

(Death Process with Immigration) Consider a population of size n, n ≥ 0, of a certain species in which individuals do not reproduce. However, new individuals immigrate into the population at a Poisson rate of γ. If the lifetime of an individual in the population is exponential with mean 1/µ, find πi, i ≥ 0, the long-run probability that the population size is i.