55. Consider a single server queuing system where customers arrive according to a Poisson process with rate λ, service times are exponential with rate μ, and customers are served in the order of their arrival. Suppose that a customer arrives and finds n − 1 others in the system. Let X denote the number in the system at the moment that customer departs. Find the probability mass function of X.

Hint: Relate this to a negative binomial random variable.