Summary

In this chapter, you learned how to perform basic simulations. We showed you how to generate pseudorandom numbers from a variety of common probability distributions. We also showed you how to perform Monte Carlo simulations including an overview of the mc2d package, and how it can be used to perform one- and two-dimensional Monte Carlo simulations in risk analysis. We also showed you how Monte Carlo methods can be applied to estimate integrals. Next, we demonstrated how importance sampling can be used to improve integral estimates. Then, we showed you how to generate random variables from unknown distributions using the rejection sampling method. Finally, we briefly showed you how simulation can be used to model physical systems by looking at Brownian motion in one- and two-dimensions. Now that you are familiar with the generation of random variables and Monte Carlo simulations, we are ready to move on to the next chapter, where we will show you how to perform numerical optimization...