ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5284 on D207: Bernoulli random boolean number

Expectation of a Bernoulli random boolean number

Formulation 0

Let $X \in \text{Bernoulli}(\theta)$ be a D207: Bernoulli random boolean number.

Then \begin{equation} \mathbb{E} X = \theta \end{equation}

Proofs

Proof 0

Let $X \in \text{Bernoulli}(\theta)$ be a D207: Bernoulli random boolean number.

This result is a particular case of R2484: Moments of a Bernoulli random boolean number. $\square$