Test 3 Ver 1 Solution

# Test 3 Ver 1 - V1 Stat 230 Quiz#3 Version 1 Solution 1 Claims for a particular class of insurance arrive as a Poisson process at the rate of 3.6

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V1 Stat 230 Quiz #3 October 27, 2004 Version 1 Solution 1. Claims for a particular class of insurance arrive as a Poisson process at the rate of 3.6 per day (Monday to Friday). (a) [2 marks] Find the probability that 4 claims arrive on a particular Monday. Since we have a Poisson process, the number of claims on a given day is Poisson with rate 3.6. Hence we have Pr( ( . 4 3 6 claims on Monday) = 3.6 4! 4 e - = 0.191) (b) [4 marks] Suppose X is the number of days in a 5 day week with exactly 4 claims. Explain, using the conditions for a Poisson process, what is the distribution of X? The number of claims in any non-overlapping days are independent. On any day we can get 4 claims or not and the probability of 4 claims on any day is given by the result in (a). Hence X is a binomial random variable with n = 5 and p e = 3.6 4! 4 - 3 6 . (c) [6 marks] Suppose that 17 claims arrive in one 5 day week. What is the probability that there were exactly 4 claims on Monday?

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## This note was uploaded on 10/21/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.

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Test 3 Ver 1 - V1 Stat 230 Quiz#3 Version 1 Solution 1 Claims for a particular class of insurance arrive as a Poisson process at the rate of 3.6

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