Let $X_1, X_2, X_3, \, \ldots \overset{d}{=} \text{Bernoulli}(\theta)$ each be a D207: Bernoulli random boolean number such that
| (i) | $\theta \in (0, 1)$ is a D5407: Positive real number |
| (ii) | $X_1, X_2, X_3, \, \ldots$ is an D2713: Independent random collection |
Then
\begin{equation}
\sum_{n = 1}^N \frac{X_n - \theta}{\sqrt{\theta (1 - \theta) N}}
\overset{d}{\longrightarrow} \text{Gaussian}(0, 1)
\quad \text{ as } \quad
N \to \infty
\end{equation}