Telephone calls to an emergency number

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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?

Reference no: EM131130841

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