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

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

Result R4825 on D5725: Simple random variable entropy

Bit entropy of a standard bernoulli number is one bit

Formulation 0

Let $X \in \text{Bernoulli}(1/2)$ be a D3999: Standard Bernoulli random boolean number.

Then \begin{equation} H_2(X) = 1 \end{equation}

Proofs

Proof 0

Let $X \in \text{Bernoulli}(1/2)$ be a D3999: Standard Bernoulli random boolean number.

This result is a particular case of R4827: Entropy of a standard bernoulli number. $\square$