Theorem 8.3.1. Exponential Probability Function.
For an exponential random variable \(X\text{,}\)
\begin{equation*}
f(x) = \lambda e^{-\lambda x},
\end{equation*}
where \(\lambda\) is a given parameter.
(Note that we will find later that \(\lambda = \frac{1}{\mu}\) or the reciprocal of the theoretical mean.)