ThmDex – An index of mathematical definitions, results, and conjectures.

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Result R3923 on D5208: Symmetric random real number
Subresult of R3922: Gaussian random real number is symmetric about its expectation

Standard gaussian random real number is symmetric about zero

Formulation 0

Let

Then

$\begin{equation} Z \overset{d}{=} - Z \end{equation}$