How do you derive the Covariance equation?

Question

How do you derive the equation Cov(x1, x2) = E[(x1-mu1)*(x2-mu2)] from the alternate equation for Covariance, Cov(x1,x2) = E(x1x2) - E(x1)E(x2) ? I am positive that I have to go from the latter to the first mentioned. I know E(x1)=mu1 and E(x2)=mu2 but I am not quite sure where to go from there.

Answer 1

Go the other way.

E[(x1-mu1)*(x2-mu2)] =
E[x1*x2-x1*mu2-x2*mu1+mu1*mu2] =
E[x1*x2] - E[x1*mu2] - E[x2*mu1] + mu1*mu2 =
E[x1*x2] - mu2*E[x1] - mu1*E[x2] + mu1*mu2 =
E[x1*x2] - mu2*mu1 - mu1*mu2 + mu1*mu2 =
E[x1*x2] - mu1*mu2=
E(x1*x2) - E(x1)*E(x2)