Consider a single-server queuing system in which arrivals follow a Poisson distribution with mean rate lambda. Service is given as follows. When a customer enters into service; with probability p the service time is zero seconds, with probability 1-p the service time is drawn from the following exponential distribution.

pe ^- ρϰ

Answer the following questions for this M/G/1 queue.
(a). Find the average service time.
(b). Find the variance of service time.
(c). Find the expected waiting time.