8 (Birth and Death with Immigration) Consider a population of a certain colonizing species Suppose that each individual produces offspring at a Poisson rate as long as it lives Moreover, suppose that new individuals immigrate into the population at a Poisson rate of If the lifetime of an individual...

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8. (Birth and Death with Immigration) Consider a population of a certain colonizing species. Suppose that each

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8. (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.

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