6.1.4 A new product (a “Home Helicopter” to solve the commuting problem)

is being introduced. The sales are expected to be determined by both media (newspaper and television) advertising and word-of-mouth advertising, wherein satisfied customers tell others about the product. Assume that media advertising creates new customers according to a Poisson process of rate D 1 customer per month. For the word-of-mouth advertising, assume that each purchaser of a Home Helicopter will generate sales to new customers at a rate of

 D 2 customers per month. Let X.t/ be the total number of Home Helicopter customers up to time t.

(a) Model X.t/ as a pure birth process by specifying the birth parameters k, for k D 0;1; : : : :

(b) What is the probability that exactly two Home Helicopters are sold during the first month?