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HW6-sol (Math 425)

# HW6-sol (Math 425) - Math 425 Section 8 Homework 6 Chapter...

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Math 425 – Section 8 Homework 6 – Chapter 4, problems 53, 55, 57, 59, 60, 74(b), 75, 79 Problem 55. A certain typing agency employs 2 typists. The average number of errors per article is 3 when typed by the ﬁrst typist and 4.2 when typed by the second. If your article is equally likely to be typed by either typist, approximate the probability that it will have no errors. Solution. First, we condition on the typist: P { no errors } = P { no errors | 1st typist } P { 1st typist } + P { no errors | 2nd typist } P { 2nd typist } We model the number of errors of the ﬁrst, resp. second, typist by a Poisson random variable with parameter λ 1 = 3, resp. λ 2 = 4 . 2. So, P { no errors } = e - 3 × 1 2 + e - 4 . 2 × 1 2 Problem 57. Suppose that the number of accidents occurring on a highway each day is a Poisson random variable with parameter λ = 3. (a) Find the probability that 3 or more accident occur today. (b) Repeat part (a) under the assumption that at least 1 accident occurs today.

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HW6-sol (Math 425) - Math 425 Section 8 Homework 6 Chapter...

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