In a recent project, I needed to generate random messages according to a Poisson distribution, where the probability that a message occurs time 't' after the previous one is lambda*e^(-lambda*t). So, given a random number generator which draws numbers from a uniform distribution, I needed to map those to the above distribution. A method that I read about was to find the CDF of the target distribution and then find the inverse into which the random numbers could be plugged in. Although this works for exponential distributions, it is not possible for every case (don't have examples off hand) -- how would the Monte Carlo methods work then?