(solution) A fisherman catches fish according to a Poisson process with rate λ = 0.6 per hour. The…

(solution) A fisherman catches fish according to a Poisson process with rate λ = 0.6 per hour. The…

A fisherman catches fish according to a Poisson process with rate λ = 0.6 per hour. The fisherman will keep fishing for two hours. If he has caught at least one fish, he quits. Otherwise, he continues until he catches at least one fish. (a) Find the probability that he stays for more than two hours. (b) Find the probability that the total time he spends fishing is between two and five hours. (c) Find the probability that he catches at least two fish. (d) Find the expected number of fish that he catches. (e) Find the expected total fishing time, given that he has been fishing for four hours.