86. In good years, storms occur according to a Poisson process with rate 3 per unit time, while in other years they occur according to a Poisson process with rate 5 per unit time. Suppose next year will be a good year with probability 0.3. LetI mage denote the number of storms during the first t time units of next year.

(a) Find .

(b) Is a Poisson process?

(c) Does have stationary increments? Why or why not?

(d) Does it have independent increments? Why or why not?

(e) If next year starts off with three storms by time , what is the conditional probability it is a good year?