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)