Problem 122E

The number of stork sightings on a route in South Carolina follows a Poisson process with a mean of 2.3 per year.

(a) What is the mean time between sightings?

(b) What is the probability that there are no sightings within three months (0.25 years)?

(c) What is the probability that the time until the first sighting exceeds six months?

(d) What is the probability of no sighting within three years?

Solution

Step 1 of 4

Let X be the distance between the successive events is a poisson process

with mean no.of events

And X is exponential with

a) We have to find the mean time between sightings

Then mean=

=

= 0.4348

Hence the mean time between sightings is 0.4348