N <- 10000 U <- runif(N) X <- U^(1/3) hist(X, breaks=50, prob=TRUE) xx <- seq(0, 1, by=0.01) lines(xx, 3*xx^2, col="red", lw=2) ## exponential lambda <- 2 U <- runif(N) X <- -log(1-U)/lambda hist(X, breaks=50, prob=TRUE) xx <- seq(0, 4, by=0.01) lines(xx, dexp(xx, rate = lambda), col="red", lw=2)