Calls are made to a telephone helpline according to a Poisson process at an average rate of 3 calls per hour. The number of questions asked by each caller has a geometric distribution (starting at 1) with mean 2.5.
Find the p.g.f. of the total number of questions asked in a period of three hours and use the p.g.f.to find variance and mean of the number of questions asked in a period of three hours.

Question

Calls are made to a telephone helpline according to a Poisson process at an average rate of 3 calls per hour. The number of questions asked by each caller has a geometric distribution (starting at 1) with mean 2.5.
Find the p.g.f. of the total number of questions asked in a period of three hours and use the p.g.f.to find variance and mean of the number of questions asked in a period of three hours.