ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5009 on D207: Bernoulli random boolean number
Bernoulli random boolean integer from a uniform random real number
Formulation 0
Let $U \in \text{Uniform} [0, 1]$ be a D4624: Standard unsigned uniform random real number such that
(i) $\theta \in [0, 1]$ is a D993: Real number
(ii) \begin{equation} X : = I_{\{ U \leq \theta \}} \end{equation}
Then \begin{equation} X \in \text{Bernoulli}(\theta) \end{equation}