ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F12694 on R5322: Adding the same random real number need not preserve equality in distribution
F12694
Formulation 0
Let $X \in \text{Gaussian}(0, 1)$ be a D211: Standard gaussian random real number such that
(i) \begin{equation} Y, Z : = - X \end{equation}
Then
(1) \begin{equation} X \overset{d}{=} Y \end{equation}
(2) \begin{equation} X + Z \overset{d}{\neq} Y + Z \end{equation}