Question no. 35

Let N(t) be the number of telephone calls to an emergency number in the interval [0,t]. We suppose that {N(t),t ≥ 0} is a Poisson process with rate λ = 50 per hour

(a) What is, according to the model, the probability that there are more calls from 8 a.m. to 9 a.m. than from 9 a.m. to 10 a.m.?

(b) Suppose that 20% of the calls are redirected to another service. Knowing that there were 60 (independent) calls during a given hour and that the first of these calls was redirected elsewhere, what is the mathematical expectation of the number of calls that were redirected over the hour in question?