Bernoulli random boolean number

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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}

Child definitions

» D2854: Poisson random natural number
» D3999: Standard Bernoulli random boolean number

Results

» 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

» R5009: Bernoulli random boolean integer from a uniform random real number

» R3261: Probability for two independent Bernoulli random numbers to coincide

» R5226: Tight lower bound on the probability for two independent Bernoulli random boolean numbers to coincide

» R5284: Expectation of a Bernoulli random boolean number

» R5283: Expectation of a standard bernoulli random boolean number