At a particular state park the forest fires occur according

At a particular state park the forest fires occur according to Poisson law, averaging 2 fires per month. a). What is the probability that there is no more than 3 fires in the next 3 months?
b). What is the probability that there are no fires for the next 2 months?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials

a)
averaging 2 fires per month
3 fires in the next 3 months mean rate be = 6 fires
Pthere is no more than 3 fires in the next 3 months, ( X < 3) = P(X=2) + P(X=1) + P(X=0)   
= e^-6 * 2 ^ 2 / 2! + e^-6 * ^ 1 / 1! + e^-6 * ^ 0 / 0!
= 0.062

b)
there is no more than 3 fires in the next 3 months mean rate be = 6 fires

Mean rate for next 2 months = 2^2 = 4
P( X = 0 ) = e ^-4 * 4^0 / 0! = 0.0183