*64. Suppose that people arrive at a bus stop in accordance with a Poisson process with rate...

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*64. Suppose that people arrive at a bus stop in accordance with a Poisson process with rate λ. The bus departs at time t. Let X denote the total amount of waiting time of all those who get on the bus at time t. We want to determine . LetI mage denote the number of arrivals by time t.

(a) What is ?

(b) Argue that .

(c) What is ?

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