Probability distribution of active calls at a telephone exchange?

Please, could someone help me with this exercise from http://www.springer.com/computer/bioinformatics/book/978-0-387-40082-2:

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.

Question

Probability distribution of active calls at a telephone exchange?

Please, could someone help me with this exercise from http://www.springer.com/computer/bioinformatics/book/978-0-387-40082-2:

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.

anonymous · Answer

$$\begin{array}{l}T=call\;duration\\lambda=arrival\;rate\\P(n)=\frac{\left(\lambda T\right)^n}{n!}e^{-\lambda T}\\end{array}$$