City buses arrive at a certain street corner

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City buses arrive at a certain street corner, between 5 a.m. and 11 p.m., according to a Poisson process with rate λ = 4 per hour. Let T₁ be the waiting time, in minutes, until the first bus (after 5 a.m.), and let M be the total number of buses between 5 a.m. and 5:15 a.m.

(a) Calculate the probability is included in the interval [0,15].

(b) What is the variance of the waiting time between two consecutive arrivals?

(c) If a person arrives at this street corner every morning at 9:05 a.m., what is the variance of the time during which she must wait for the bus? Justify.

Reference no: EM131130893

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