My textbook claims that $cov(X, Y) = E((X - E(X))(Y - E(Y)))$.
It then claims that, multiplying this out and using linearity, we have an equivalent expression $cov(X, Y) = E(XY) - E(X)E(Y)$.
My attempt of deriving this is as follows:
$$ cov(X, Y) = E((X - E(X))(Y - E(Y))) = E(XY - X E(Y) - Y E(X) + E(X) E(Y)) = E(XY) - E(X) E(Y) - E(Y) E(X) + E(X) E(Y) = E(XY) - E(X) E(Y) $$
Please give feedback on whether this is correct.
Thank you.