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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.7 - Problem 9e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.7 - Problem 9e

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# The number of traffic accidents at a certain intersection

ISBN: 9780073401331 38

## Solution for problem 9E Chapter 4.7

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

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

Step 3 of 6

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