Question

Suppose that the number of hurricanes in a certain region occur in accordance with a Poisson process with rate of 0.1 per month.

(a) What is the probability that the next hurricane will occur in less than two years?

(b) What is the probability that at least nine of the next ten years has no hurricanes?

Answer 1

a)expected number of hurricanes in two years (24 months) =24*0.1 =2.4

probability that the next hurricane will occur in less than two years=1-P(no hurricane) =1-(e^-2.42.4⁰/0!) =0.9093

b)

expected number of hurricane in a year(12 months)= 0.1*12 =1.2

P(no hurricane in a year) =e^-1.2*1.2⁰/0! =0.3012

therefore from binomial distribution with parameter n=10 and p=0.3012

probability that at least nine of the next ten years has no hurricanes =P(X=9)+P(X=10)

=(10C9)*(0.3012)⁹(1-0.3012)¹+(10C10)*(0.3012)¹⁰(1-0.3012)⁰ =0.000149