Exercises 6.10: 15, 23

Exercises 7.8: 17, 35

And:

1. Suppose $X$ and $Y$ are jointly continuous random variables with joint probability density function $f_{X,Y}(x,y) = \begin{cases}8xy,& \text{if } 0 < x < y < 1,\\ 0,& \text{otherwise}.\end{cases}$ Find each of the following:
   1. $E(X)$
   2. $E(Y^2)$
   3. $E(XY^3)$