what is the covXYSolutionDefinition Let X and Y be random va

what is the cov(X,Y)?

Solution

Definition. Let X and Y be random variables (discrete or continuous!) with means _X and _Y. The covariance of X and Y, denoted Cov(X,Y) or _XY, is defined as:

Cov(X,Y)=XY=E[(XX)(YY)]

That is, if X and Y are discrete random variables with joint support S, then the covariance of X and Y is:

Cov(X,Y)=(x,y)S(xX)(yY)f(x,y)

And, if X and Y are continuous random variables with supports S₁ and S₂, respectively, then the covariance of X and Y is:

Cov(X,Y)=S2S1(xX)(yY)f(x,y)dxdy