In a certain town up in the mountains there are no bears at time t = 0. Brown bears and grizzly bears arrive according to two independent Poisson processes with respective arrival rates and .

(a) Compute the probability that the first bear arriving in town is a grizzly bear.

(b) Suppose that the first bear arriving in town is a grizzly bear. How long does it take on average before this bear arrives? Give a reason for your answer.

(c) Find the probability that between two consecutive grizzly bears there arrive exactly r N₀ brown bears. Justify your answer