Let $X_1, X_2, X_3, \ldots \in \text{Bernoulli}(1/2)$ each be a D3999: Standard Bernoulli random boolean 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 - \frac{1}{2}}{\sqrt{N / 4}}
\overset{d}{\longrightarrow} \text{Gaussian}(0, 1)
\quad \text{ as } \quad
N \to \infty
\end{equation}