Let Y be a random variable with probability density function given by
$f(y) = \begin{cases} 2(1 - y), & 0 \le y \le 1, \\ 0, & \text{elsewhere.} \end{cases}$
Use the method of transformation to find the densities of $U_1$, $U_2$, and $U_3$.
(a) $U_1 = 7Y - 9$
$f_{U_1}(u) = \begin{cases} & \le u \le \\ & \text{elsewhere} \end{cases}$
(b) $U_2 = 9 - 7Y$
$f_{U_2}(u) = \begin{cases} & \le u \le \\ & \text{elsewhere} \end{cases}$
(c) $U_3 = Y^2$
$f_{U_3}(u) = \begin{cases} & \le u \le \\ & \text{elsewhere} \end{cases}$