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Formulation F11375 on R4875: Popoviciu's inequality
F11375
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}