E[(X-E(X))(Y-E(Y))] is called covariance of random variables x and y, and it is denoted as COV(X, y), that is, COV(X, y) = E [(x-e (x)) (y-e (y)) t].

That is, COV(X, y) = e (xy)-e (x) e (y);

Another solution: given the variances d (x) and d (y) of the random variable x, y, COV(X, Y)=[D(X)+D(Y)-D(X+Y)]/2.

In addition, in mathematics, discrete mathematical posets mean covering.

In a poset

Note: cover A = {

COV(X)=E[(X-E(X))(X-E(X))^T]

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. ?

The relationship between covariance and variance is as follows: 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).

References:

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