Suppose that calls arrive at a telephone exchange according to a Poisson process with parameter lambda. If the lengths of the various calls are identical and independent random variables, each with cumulative distribution function F(x), find the probability distribution of the number of calls in progress at any time.

I really don't know how to relate the continuous distribution to a discrete one. I've tried to work it out the same way you achieve P(n) in a M/M/1 queue, and came up to something like P(n) = (1-rho)*rho^n, where rho = lambda * E(f). Then I wrote a Java program to simulate the situation and compare the simulation frequencies with this result, and they're rather different. Moreover, the book proposes the exercise after a chapter on 1-variable probability distributions, with no mention of queue theory or Markov processes (I know about that cause I'm brushing up my statistics).

I'm pretty sure I'm missing something simple, any idea please? Thanks in advance.