Let X and Y be continuous rv with joint density function Ple

Let X and Y be continuous r.v. with joint density function

Please give two different formulas that show how to find cov(X,Y) **No need to do the actual integration**
One formula should use the definition of cov (which should have one definite double integral) and the other uses the short cut formula for finding cov. (which should have difference between two definite double integrals).

Thank you

Solution

Cov(x,y)=

E(x)=x

E(y)=

E(xy)=

Short cut formula is:

Cov(x,y)=E(xy)-E(x)E(Y)