Question

In a particular location, earthquakes occur according to a Poisson process, at an average rate of 0.25 earthquakes per week. Suppose we observe this location for a year (52 weeks). What is the probability that we will observe exactly the expected number of earthquakes? Select one: a. 0.77 b. 0.11 c. 0.43 d. 0.23 e. 0.57

Answer 1

Given: In a particular location, earthquakes occurs according to the Poisson process at an average rate of 0.25 earthquakes per week.

Let X be the number of earthquakes occurs in a year ie t=52

Therefore,

Where the expected value is

ie

Therefore the probability that we will observe exactly the expected number of earthquakes in a year is given by

## by using Excel function:. =POISSON.DIST(13,13,0)

Hence

Therefore correct choice is b)