方差 协方差

Posted 2020-10-07 rsapaper

 

【方差 协方差】
方差 variance
协方差 covariance
https://en.wikipedia.org/wiki/Variance
方差 一个随机变量的方差描述的是它的离散程度，一个实随机变量的方差，也成为它的二阶矩或二阶中心动差。
Informally, it measures how far a set of (random) numbers are spread out from their average value.
Variance has a central role in statistics, where some ideas that use it include descriptive statistics,
statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself.
方差是协方差的一种特殊情况，即当两个变量是相同的情况。

 

E(X)=u E(Y)=v
cov(X,Y)=E((X-u)(Y-v))
=E(X*Y)-uv

如果X 与Y 是统计独立的，那么二者之间的协方差就是0，这是因为
E(X*Y)=E(X)*E(Y)=uv
但是反过来并不成立，即如果X 与Y 的协方差为0，二者并不一定是统计独立的。