Statistics of small bits and pieces (please add at any time)

Knowledge point 1: Covariance and correlation coefficient

[Definition 1]
The covariance of random variables X and Y is recorded as cov(X,Y), as follows:
$$cov(X,And)=And\left[\right(X-EX\left)\right(Y-EY)]$$
令 $X^{\ast }=\frac{X-EX}{\sqrt{DX}}$, $Y^{\ast }=\frac{Y-EY}{\sqrt{DY}}$ , 称
$$r_{XY}=E{X}^{\ast }{Y}^{\ast }=\frac{cov(X,Y)}{\sqrt{DX}\sqrt{DY}}$$
Is the correlation coefficient of random variables X and Y. The correlation coefficient values [-1,1], the measured X, Y of the linear correlation . If $r_{XY}=0$ , it is said that X and Y are not related.

Correlation is a standardized format for covariance . Covariance itself is difficult to compare. For example: if we calculate the covariance of salary ($) and age (years), because these two variables have different measures, we will get different covariances that cannot be compared. To solve this problem, we calculate the correlation to get a value between -1 and 1, we can ignore their different metrics.