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?

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