10. Consider a birthdeath process whose birth and death rates satisfy = . If the initial population size is I , show that the

10. Consider a birth–death process whose birth and death rates satisfy λ = μ. If the initial population size is I , show that the time T until the extinction of the process has distribution function P(T ≤ t ) =



λt

λt + 1

J for t > 0, and deduce that, as I → ∞, the random variable UI = λT/I has limiting distribution function given by P(UI ≤ t )→ e−1/t for t ≥ 0.