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 unit time. Suppose next year will be a good year per with probability 0.3. Let N(t) denote the number of storms during the first time units of next year. (a) Find P{N(t) = n}. (b) Is {N(t)} a Poisson process? (c) Does {N(t)) 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 t = 1, what is the conditional probability it is a good year?

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