方差等于平方的期望-期望的平方,证明如下
[vec{x}=
left[
egin{matrix}
x_1\
x_2\
cdots\
x_n\
end{matrix}
ight] \
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}-2cdot overline{x}cdot x_i+overline{x}^2)\
=E(x_{i}^{2})-2cdot overline{x}cdot E(x_i)+overline{x}^2\
=E(x_{i}^{2})-overline{x}^2\
=E(vec{x}cdotvec{x}^T)-E^2(vec{x})
]