## Definition ==Joint Moments== are expected values of products of powers of two or more random variables. The joint moment of order $(m, n)$ for random variables $X$ and $Y$ is: $ E[X^m Y^n] = \iint x^m y^n f(x, y)\, dx\, dy $ The most important joint moment is $E[XY]$, which is used to compute the covariance. > [!example]- If $X$ and $Y$ are independent with $E[X] = 3$ and $E[Y] = 5$, what is $E[XY]$? > For independent random variables, $E[XY] = E[X] \cdot E[Y]$: > $ E[XY] = 3 \times 5 = 15 $