Excluding empty lines, what is the average line length?

Now the formula we want is:

This example plots the shape of the Poisson distribution. It's intended to give you a feel for what the arrival distribution looks like. The plot shows the probability of n arrivals on or before time t. The four series shown depict the distributions of the arrival of the n^th customer by time t, for n = 0 to 3.

The plot for n = 0 shows the probability of zero arrivals as a function of time. In other words, for t=5 say, it answers the question "What's the probability that we have no arrivals?" For high l, this plot moves in towards 0 — more probability is concentrated toward 0. This happens because of the first factor of the Poisson distribution, (lt)^k, which for k = 0 becomes (lt)⁰. At t = 0, this is 0⁰ = 1. The second factor, e^-lt, then prevails.

For other values of n, the two factors compete. Since the first is a simple power, and the second is an exponential, the second always wins, eventually. Thus the shape of the distribution for n > 0 is humped, with the maximum occurring at greater t as n increases.