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Statistics / Probability and Statistical Inference 9 / Chapter 5.4 / Problem 18E

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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The number of cracks on a highway averages 0.5 per mile

Chapter 5, Problem 18E

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QUESTION:

The number of cracks on a highway averages 0.5 per mile and follows a Poisson distribution. Assuming independence (which may not be a good assumption; why?), what is the probability that, in a 40-mile stretch of that highway, there are fewer than 15 cracks?

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QUESTION:

The number of cracks on a highway averages 0.5 per mile and follows a Poisson distribution. Assuming independence (which may not be a good assumption; why?), what is the probability that, in a 40-mile stretch of that highway, there are fewer than 15 cracks?

ANSWER:

Problem 18E

The number of cracks on a highway averages 0.5 per mile and follows a Poisson distribution. Assuming independence (which may not be a good assumption; why?), what is the probability that, in a 40-mile stretch of that highway, there are fewer than 15 cracks?

Step by Step Solution

Step 1 of 3

Suppose that are independent random variable then the MGF is is,

Let have a Poisson distribution with .

The MGF of is,

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