416-10 - X Problem 4(Problem 66 p 358 Policyholders of a...

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Denker Spring 2010 416 Stochastic Modeling - Assignment 10 Due Date: Monday, April 5, 2010 Problem 1: (Problem 40, p. 352) Let N 1 and N 2 be two independent Poisson processes. Show that N ( t ) = N 1 ( t )+ N 2 ( t ) is a Poisson process and determine the rate of N . Problem 2: (Problem 42, p. 352) Let N ( t ) be a Poisson process with rate λ = 4. Let S n denote the time when the n -th event occurs. Find E [ S 4 ], E [ S 4 | N (1) = 2], and E [ N (4) - N (2) | N (1) = 3]. Problem 3: (Problem 50, p. 354) Customers arrive at a train station according to a Poisson process with rate λ = 7. The trains run according to a uniform distribution within one hour of each other. Suppose that a train just left the station. Let X be the number of passengers who get on the next train. Find the expectation and variance of
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Unformatted text preview: X . Problem 4: (Problem 66, p. 358) Policyholders of a certain insurance company have accidents at times distributed ac-cording to a Poisson process with rate λ . The amount of time from when the accident occurs until the claim is made has distribution G . Find the probability that there are exactly n incured but as yet unreported claims at time t . Problem 5: (Problem 60, p. 356) Customers arrive at a bank at Poisson rate λ . Suppose 2 customers arrived during the ±rst hour. What is the probability that (a) both arrived during the ±rst 20 minutes? (b) at least one arrived during the ±rst 20 minutes?...
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