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Take this joint distribution table as an example:
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Extended data:
If two random variables X and Y are independent of each other, then E[(X-E(X))(Y-E(Y))]=0, so if the above mathematical expectation is not zero, then X and Y are not independent of each other, that is, there is a certain relationship between them.
There is the following relationship between covariance and variance:
D(X+Y)=D(X)+D(Y)+2Cov(X，Y)
D(X-Y)=D(X)+D(Y)-2Cov(X，Y)
Covariance has the following relationship with expected value:
Cov(X，Y)=E(XY)-E(X)E(Y).
Properties of covariance:
( 1)Cov(X，Y)=Cov(Y，X)；
(2)Cov(aX, bY)=abCov(X, y), (a, b are constants);
(3)Cov(X 1+X2，Y)=Cov(X 1，Y)+Cov(X2，Y).
As can be seen from the definition of covariance, Cov(X, X)=D(X), Cov(Y, Y)=D(Y).