ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4875 on D3161: Random real number
Popoviciu's inequality
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \exists \, a, b \in \mathbb{R} : \mathbb{P}(X \in [a, b]) = 1 \end{equation}
Then \begin{equation} \text{Var} X \leq \frac{(b - a)^2}{4} \end{equation}
Also known as
Popoviciu upper bound to variance of bounded random real number
Subresults
▶ R4876: Interval length upper bound to variance of bounded random real number