42. Dry and wet seasons alternate, with each dry season lasting an exponential time with rate λ and each wet season an exponential time with rate μ. The lengths of dry and wet seasons are all independent. In addition, suppose that people arrive to a service facility according to a Poisson process with rate v. Those that arrive during a dry season are allowed to enter; those that arrive during a wet season are lost. LetI mage denote the number of lost customers by time t.

(a) Find the proportion of time that we are in a wet season.

(b) Is Image a (possibly delayed) renewal process?

(c) Find Image