Let $X_1, \, \ldots, \, X_N \overset{d}{=} \text{Bernoulli}(\theta)$ each be a D207: Bernoulli random boolean 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{Binomial}(N, \theta) \end{equation}