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