*43. Consider an system in which the first customer in a busy period has the service distribution and all others have distribution . Let C denote the number of customers in a busy period, and let S denote the service time of a customer chosen at random.

Argue that

(a) Image.

(b) Image where has distribution Image.

(c) Use

(a) and

(b) to show that Image, the expected length of a busy period, is given by Image

(d) Find .