# Poisson Process Question

• Nov 27th 2011, 11:58 AM
KelvinScale
Poisson Process Question
Hi everyone, I am stuck on this Poisson process question.

Lightning strikes a forest region following a poisson process with 3 strikes per day. Each strike has a 0.5 probability of starting a fire. Find the probability that there are at least 5 fires in a 30 day period. The answer is 0.468

The way I appropached this problem was defining X as the number of lightning strikes, and Y as the number of fires. Then using a property in the textbook, the marginal probability was defined as a poisson process following 0.05(lambda). I am not sure which lambda I should use to calculate (P>=5). Should I take 1.5 (average fire per day) or 4.5 (averages fires over 30 days)?

Any insight would be much appreciated! Thanks!
• Nov 27th 2011, 11:47 PM
CaptainBlack
Re: Poisson Process Question
Quote:

Originally Posted by KelvinScale
Hi everyone, I am stuck on this Poisson process question.

Lightning strikes a forest region following a poisson process with 3 strikes per day. Each strike has a 0.5 probability of starting a fire. Find the probability that there are at least 5 fires in a 30 day period. The answer is 0.468

The way I appropached this problem was defining X as the number of lightning strikes, and Y as the number of fires. Then using a property in the textbook, the marginal probability was defined as a poisson process following 0.05(lambda). I am not sure which lambda I should use to calculate (P>=5). Should I take 1.5 (average fire per day) or 4.5 (averages fires over 30 days)?

Any insight would be much appreciated! Thanks!

Please review this question some of the data given must be wrong. With the data given you have a 6-sigma problem and the probability of at least 5 fires in 30 days is indistinguishable from 1.

CB