Let $X_1, \ldots, X_N \in \text{Poisson}(\theta)$ each be a D2854: Poisson random natural number such that
| (i) | $X_1, \ldots, X_N$ is an D3842: Uncorrelated random collection |
Then
\begin{equation}
\sum_{n = 1}^N X_n
\overset{d}{=} \text{Poisson} (N \theta)
\end{equation}