ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D5723
Simple random variable
Formulation 1
A D202: Random variable $X : \Omega \to \mathcal{X}$ is simple if and only if
(1) $\{ X(\omega) : \omega \in \Omega \} \neq \emptyset$ is a D17: Finite set
(2) \begin{equation} \forall \, x \in \mathcal{X} : \mathbb{P}(X = x) > 0 \end{equation}