A certain random variable X has the probability density function (pdf) given by f X (x)={ x 1, 1x, 1x0 0x1 and f X (x)=0, otherwise.

(a) Show that the cumulative distribution function may be expressed as F X (X) = {0, x<-1, 1/2(1-x)^(2), -1<=x<=0, 1 - 1/2(1 - x)^(2), 0<=x<=1, 1, x>1)

(b) Given a standard uniform random variable U, give an algorithm to generate the random variable X using the result in part a.