Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) | \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation} |
(ii) | \begin{equation} \mu : = \mathbb{E} X \end{equation} |
(iii) | \begin{equation} \sigma : = \text{Std} X \end{equation} |
Then
(1) | \begin{equation} \mathbb{E} \left( \frac{X - \mu}{\sigma} \right) = 0 \end{equation} |
(2) | \begin{equation} \text{Var} \left( \frac{X - \mu}{\sigma} \right) = 1 \end{equation} |