向量期望与方差的关系
方差等于平方的期望-期望的平方，证明如下
\[\vec{x}=
\left[
\begin{matrix}
x_1\\
x_2\\
\cdots\\
x_n\\
\end{matrix}
\right] \\
\overline{x}=\frac{\sum_{i=1}^{n}{x_i}}{n}=E(\vec{x}) \\
D(\vec{x})=\sum_{i=1}^{n}{(x_i-\overline{x})^2}\\
=E((x_i-\overline{x})^2)\\
=E(x_{i}^{2}-2\cdot \overline{x}\cdot x_i+\overline{x}^2)\\
=E(x_{i}^{2})-2\cdot \overline{x}\cdot E(x_i)+\overline{x}^2\\
=E(x_{i}^{2})-\overline{x}^2\\
=E(\vec{x}\cdot\vec{x}^T)-E^2(\vec{x})
\]
