# 1 markov chains let xn be a markov chain and suppose

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Unformatted text preview: CISES 99 2.56. Policy holders of an insurance company have accidents at times of a Poisson process with rate . The distribution of the time R until a claim is reported is random with P (R r) = G(r) and ER = ⌫ . (a) Find the distribution of the number of unreported claims. (b) Suppose each claim has mean µ and variance 2 . Find the mean and variance of S the total size of the unreported claims. 2.57. Suppose N (t) is a Poisson process with rate 2. Compute the conditional probabilities (a) P (N (3) = 4|N (1) = 1), (b) P (N (1) = 1|N (3) = 4). 2.58. For a Poisson process N (t) with arrival rate 2 compute: (a) P (N (2) = 5), (b) P (N (5) = 8|N (2) = 3, (c) P (N (2) = 3|N (5) = 8). 2.59. Customers arrive at a bank according to a Poisson process with rate 10 per hour. Given that two customers arrived in the ﬁrst 5 minutes, what is the probability that (a) both arrived in the ﬁrst 2 minutes. (b) at least one arrived in the ﬁrst 2 minutes. 2.60. Suppose that the number of calls per hour to an answering service...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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