ThmDex – An index of mathematical definitions, results, and conjectures.
F13433
Formulation 2
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \exists \, a \in \mathbb{R} : \mathbb{P}(X = a) = 1 \end{equation}
Then \begin{equation} \forall \, t \in \mathbb{R} : \mathbb{E} \left( e^{i t X} \right) = e^{i t a} \end{equation}