ThmDex – An index of mathematical definitions, results, and conjectures.
F8878
Formulation 0
Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
Let $t \in \mathbb{R}$ be a D993: Real number.
Then \begin{equation} \mathbb{E}(e^{i t Z}) = e^{- t^2 / 2} \end{equation}