方差等於平方的期望-期望的平方，證明如下
\[\vec{x}= \left[ \begin{matrix} x_1\\ x_2\\ \cdots\\ x_n\\ \end{matrix} \right] \\ \overline{x}=\frac{\sum_{i=1}^{n}{x_i}}{n}=E(\vec{x}) \\ D(\vec{x})=\sum_{i=1}^{n}{(x_i-\overline{x})^2}\\ =E((x_i-\overline{x})^2)\\ =E(x_{i}^{2}-2\cdot \overline{x}\cdot x_i+\overline{x}^2)\\ =E(x_{i}^{2})-2\cdot \overline{x}\cdot E(x_i)+\overline{x}^2\\ =E(x_{i}^{2})-\overline{x}^2\\ =E(\vec{x}\cdot\vec{x}^T)-E^2(\vec{x}) \]