Gamma problem

[mamadou]

Can sombody explain How to solve this problem?

Assume that the number of airplane crashes during a year follows a Poisson distribution with parameter lambda = 2 per year. Find the probability that the time between the next two crashes is at least 4 months.

[wy3310]

Can sombody explain How to solve this problem?

Assume that the number of airplane crashes during a year follows a Poisson distribution with parameter lambda = 2 per year. Find the probability that the time between the next two crashes is at least 4 months.



You can use Poisson distribution with parameter lambda=2/3 (2*4/12) to solve this problem.P[N(2/3)≤1]=P[N(2/3)=0]+P[N(2/3)=1]=e^(-2/3)+(2/3)e^(-2/3)=0.8557

[engelbmj]

Since Poisson and Exponential are related (Exponential mean is inverse of Poisson mean), you can simply use Exponential to solve, with beta (the Exponential mean) = 1/2 year. This yields answer of .846. Someone please correct me if I'm wrong.