(Birth and Death with Immigration) Consider a population of a certain colonizing species. Suppose that each individual produces offspring at a Poisson rate λ as long as it lives. Moreover, suppose...

(Birth and Death with Immigration) Consider a population of a certain colonizing species. Suppose that each individual produces offspring at a Poisson rate λ as long as it lives. Moreover, suppose that 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, starting with no individuals, find the expected length of time until the population size is 3.