# Example of higher random vector moments

$$E\left[\vec{X}\right] = \left[\begin{array}{cccc} E\left[\vec{X}_1\right] & E\left[\vec{X}_2\right] & \cdots & E\left[\vec{X}_m\right]\end{array}\right]^T\in\mathbb{R}^m$$
• $$\vec{X} = \left[\begin{array}{cc}U & V\end{array}\right]^T$$.
• $$P\left[U = u, V = v\right] = \cases{\frac{3}{2}x^2 + y & 0 < x,y < 1\\ 0 & otherwise}$$.
How would I find $$E\left[\vec{X}^n\right]$$ & what would the answer be for a small example like $$E\left[\vec{X}^3\right]$$?