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Test 3 Ver 2 Solution

# Test 3 Ver 2 Solution - V2 Stat 230 Quiz#3 Version 2...

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V2 Stat 230 Quiz #3 Version 2 Solution 1. Claims for a particular class of insurance arrive as a Poisson process at the rate of 2.6 per day (Monday to Friday). (a) [2 marks] Find the probability that 3 claims arrive on a particular Monday. Since we have a Poisson process, the number of claims on a given day is Poisson with rate 2.6. Hence we have 3 2.6 2.6 Pr(3claims on Monday)= ( 0.218) 3! e - = (b) [4 marks] Suppose X is the number of days in a 5 day week with exactly 3 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 3 claims or not and the probability of 3 claims on any day is given by the result in (a). Hence X is a binomial random variable with n = 5 and 3 2.6 2.6 = 3! p e - (c) [6 marks] Suppose that 14 claims arrive in one week. What is the probability that there were exactly 3 claims on Monday? Let

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Test 3 Ver 2 Solution - V2 Stat 230 Quiz#3 Version 2...

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