Poisson Distribution

A discrete probability distribution \(P(\lambda)\) having the PMF
\[ p_{\lambda}(k) = \frac{\lambda^k e^{-\lambda}}{k!} \]
where the exclamation mark represents the factorial, that governs the probability that \(k\) events that occur at a rate \(\lambda\) and whose arrival is independent of previous arrival times will occur in a single unit of time.