Let $X_1, X_2, X_3, \ldots \in \text{Poisson}(\theta)$ each be a D2854: Poisson random natural number such that

(i)	$X_1, X_2, X_3, \ldots$ is an D2713: Independent random collection

Then \begin{equation} \sum_{n = 1}^N \frac{X_n - \theta}{\sqrt{\theta N}} \overset{d}{\longrightarrow} \text{Gaussian}(0, 1) \quad \text{ as } \quad N \to \infty \end{equation}