Events occur according to a Poisson process with rate 2 per

Events occur according to a Poisson process with rate 2 per hour. What is the probability that exactly 3 event occur between the times 8am and 10am?

Solution

Given X follows Poisson distribution with mean=2*2=4 in two hours

P(X=x)=(4^x)*exp(-4)/x! for x=0,1,...

So the probability is

P(X=3) =(4^3)*exp(-4)/6 =0.1953668