Let $X_1 \in \text{Poisson}(\theta_1), \ldots, X_N \in \text{Poisson}(\theta_N)$ each be a D2854: Poisson random natural number such that

(i)	$X_1, \ldots, X_N$ is an D2713: Independent random collection

Then \begin{equation} \sum_{n = 1}^N X_n \overset{d}{=} \text{Poisson} \left( \sum_{n = 1}^N \theta_n \right) \end{equation}