Theorem 8.2.1. Poisson Probability Function.
Assume X measures the number of successes in an interval [0,T] within some Poisson process. Then, with \(\mu\) as a needed parameter
\begin{equation*}
f(x) = \frac{\mu^x e^{-\mu}}{x!}
\end{equation*}
for \(R = \{ 0, 1, 2, ... \}.\)