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The number of traffic accidents at a certain intersection

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 9E Chapter 4.7

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year.

a. Find the mean waiting time between accidents.

b. Find the standard deviation of the waiting times between accidents.

c. Find the probability that more than one year elapses between accidents.

d. Find the probability that less than one month elapses between accidents.

e. If no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?

Step-by-Step Solution:

Solution

Step 1 of 6

The no.of traffic accidents follows a poisson process with mean of 3 accidents per year

Here

The pmf of exponential distribution is

The CDF of exponential distribution is

Let X be the waiting time between the accidents


Step 2 of 6

Chapter 4.7, Problem 9E is Solved
Step 3 of 6

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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The number of traffic accidents at a certain intersection