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!