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[ 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}) ]

原文地址:https://www.cnblogs.com/Higgerw/p/14913237.html