Problem 2. Let X, (i = 1, 2, 3) be independent random variables
distributed Gamma (i,2) and let Fi be their respective cumulative
distribution functions. Consider a random variable X, whose
cumulative distribution function equals Fx (x) = F1 (x)F2 (x) F3
(x). Generate 1000 samples of such a r.v. and make a histogram of
the simulated values. Compare with the plot of the density. Hint:
What I expect should be better than just taking the inverse of the
directly computed F x.