Let $T_1, \, \ldots, \, T_N \overset{d}{=} \text{Exponential}(\theta)$ each be an D214: Exponential random positive real number such that

(i)	$T_1, \, \ldots, \, T_N$ is an D2713: Independent random collection

A D5722: Random positive real number $X \in \text{Random}(0, \infty)$ is an Erlang random positive real number with parameter $(N, \theta)$ if and only if \begin{equation} X \overset{d}{=} \sum_{n = 1}^N T_n \end{equation}