ThmDex – An index of mathematical definitions, results, and conjectures.
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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
▶ D2854: Poisson random natural number
▶ D3999: Standard Bernoulli random boolean number
Results
▶ R5284: Expectation of a Bernoulli random boolean number
▶ R5283: Expectation of a standard bernoulli random boolean number
▶ R5679: Given convex coefficient parameters, equal allocation maximizes uncorrelated finite Bernoulli product
▶ R2484: Moments of a Bernoulli random boolean number
▶ R4791: Probability for two independent standard Bernoulli random boolean numbers to coincide
▶ R2483: Variance of Bernoulli random boolean number
▶ R4947: Variance of standard Bernoulli random boolean number