Stochastic

# 236 customers arrive at an automated teller machine

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Unformatted text preview: yden ﬁre department is ready to respond now. Find the probability distribution for the number of calls they will handle before they have to ask for help from the Ithaca ﬁre department. 2.27. A math professor waits at the bus stop at the Mittag-Le✏er Institute in the suburbs of Stockholm, Sweden. Since he has forgotten to ﬁnd out about the bus schedule, his waiting time until the next bus is uniform on (0,1). Cars drive by the bus stop at rate 6 per hour. Each will take him into town with probability 1/3. What is the probability he will end up riding the bus? 2.28. The number of hours between successive trains is T which is uniformly distributed between 1 and 2. Passengers arrive at the station according to a Poisson process with rate 24 per hour. Let X denote the number of people who get on a train. Find (a) EX , (b) var (X ). 2.29. Consider a Poisson process with rate and let L be the time of the last arrival in the interval [0, t], with L = 0 if there was no arrival. (a) Comp...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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