ThmDex – An index of mathematical definitions, results, and conjectures.
F9693
Formulation 1
Let $X, A, B \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that
(i) \begin{equation} A \overset{a.s.}{\leq } B \end{equation}
Then \begin{equation} \mathbb{P}(X \leq A) \leq \mathbb{P}(X \leq B) \end{equation}