ABSTRACT
This chapter introduces one very common type of probabilistic model, simulation. A simulation, in general, is any model that uses random numbers. Often simulations are used to imitate some type of real world behavior, but this does not have to be the case. The chapter focuses on Monte Carlo simulations. These simulations consist of three basic steps: construct a model that uses random numbers; evaluate, or “run,” the model many times using different random numbers each time; and statistically analyze the results. The chapter illustrates some of the basic concepts involved with a Monte Carlo simulation with different examples. It shows how simulations can be used to approximate the solutions to three famous problems in elementary probability: the Monty Hall Problem, the Birthday Problem, and Buffon’s Needle Problem. Simulation is a useful tool for modeling the interaction of random events. One of the most important concepts used in modeling random events is the random variable.
