1 markov chains let xn be a markov chain and suppose

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online