ThmDex – An index of mathematical definitions, results, and conjectures.
F8873
Formulation 0
Let $X \in \text{Gaussian}(\mu, \sigma)$ be a D210: Gaussian random real number.
Let $t \in \mathbb{R}$ be a D993: Real number.
Then \begin{equation} \mathbb{E}(e^{i t X}) = e^{i \mu t - \sigma^2 t^2 / 2} \end{equation}