Question

Cliams on a gruop of people rise randomly and independently of each other through time at an average rate of 2 per month. Calculate the probability that 30 claims arise in a period of one year

Answer 1

This is a Poisson distribution with $\mu=2*12=24.$

$P(X=30)=e^{-24}\frac{24^{30}}{30!}=0.0363.$