(a) Generate 1,000 random numbers from the triangular distribution. (The PDF is given in equation (3.28).) Produce a histogram and compute some summary statistics.

\(f_X(x)= \begin{cases}1-|x| & \text { for }-1

(b) Let \(Y=8 X^{3}\), where \(X\) has the triangular distribution. (The \(\mathrm{PDF}\) of \(Y\) is given in equation (3.29).)

\(f_Y(y)= \begin{cases}1 /\left|6 y^{2 / 3}\right|-1 /\left|12 y^{1 / 3}\right| & \text { for }-8

Generate 1,000 random numbers corresponding to the random variable \(Y\). (There are different ways of doing this. Which way do you think is better, and why?) Produce a histogram and compute some summary statistics.