Answer
a) {$\frac{1}{4}, \frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}$}
Work Step by Step
Note that there are only 6 possible orders that we can make using only 2 pieces of wood:
1) $\frac{1}{8} + \frac{1}{8} = \frac{1}{4}$
2) $\frac{1}{8} + \frac{1}{4} = \frac{3}{8}$
3) $\frac{1}{8} + \frac{3}{8} = \frac{1}{2}$
4) $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$
5) $\frac{1}{4} + \frac{3}{8} = \frac{5}{8}$
6) $\frac{3}{8} + \frac{3}{8} = \frac{3}{4}$
The value $\frac{1}{2}$ appears twice, so there are only 5 possible values for the random variable: {$\frac{1}{4}, \frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}$}
