ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
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▼ Zermelo-Fraenkel set theory
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▼ Random simple number
▼ Random Boolean number
Definition D207
Bernoulli random boolean number
Formulation 0
A D3628: Random Boolean number $X \in \text{Random} \{ 0, 1 \}$ is a Bernoulli random boolean number with parameter $\theta \in [0, 1]$ if and only if
(1) \begin{equation} \mathbb{P}(X = 1) = \theta \end{equation}
(2) \begin{equation} \mathbb{P}(X = 0) = 1 - \theta \end{equation}
Children
▶ Poisson random natural number
▶ Standard Bernoulli random boolean number
Results
▶ Expectation of a Bernoulli random boolean number
▶ Expectation of a standard bernoulli random boolean number
▶ Moments of a Bernoulli random boolean number
▶ Probability for two independent standard Bernoulli random boolean numbers to coincide
▶ Variance of Bernoulli random boolean number
▶ Variance of standard Bernoulli random boolean number