1. If the joint probability density of X and Y is given by \[ f(x, y) = \begin{cases} \frac{2}{7}(x+2y), & \text{for } 0 < x < 1, 1 < y < 2; \\ 0, & \text{elsewhere}. \end{cases} \] Find the expected value of $g(x, y) = x/y^3$. (15%)