p.d.f. of random variable X:
f(x) = \begin{cases} {1\over 2}x & \text{for } 0 < x < 2\\[10pt] 0 &\text{otherwise} \end{cases}
Suppose that $Y = X(2-X)$. How do you determine the c.d.f. and the p.d.f. of $Y$?
Also, how do you determine the p.d.f. of $Y = 4-X^3$