ThmDex – An index of mathematical definitions, results, and conjectures.
F11634
Formulation 0
Let $X_1, X_2, X_3, \ldots \in \text{Bernoulli}(\theta)$ each be a D207: 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 - \theta}{\sqrt{\theta (1 - \theta) N}} \overset{d}{\longrightarrow} \text{Gaussian}(0, 1) \quad \text{ as } \quad N \to \infty \end{equation}