ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5409 on D210: Gaussian random real number
Expectation of the absolute value of a centred standard gaussian random real number
Formulation 0
Let $Z \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number.
Then \begin{equation} \mathbb{E} |Z| = \sqrt{\frac{2}{\pi}} \end{equation}