Computers and Probability

Abstract

As we have seen in the previous chapter, a modern computer with a good random number generator allows you to do simulations and Monte Carlo calculations, and in so doing enables you to see many of the fundamental laws of probability in action. Lots of the results in probability, such as the Law of Large Numbers, require a large number of trials before something nice happens. With the computer, we can simulate a large number of trials in a very short time, so we should be able to test out our results and even perhaps discover new ones by playing around with probability and the computer. In this chapter, we want to do a little of this, so some familiarity with a personal computer and a programming language will be assumed. We are going to write some elementary algorithms for simulation and Monte Carlo procedures illustrating examples discussed in preceding chapters. An algorithm is just a step-by-step description of the solution of a problem in a finite number of steps. We are going to write the algorithm in pseudocode, that is, ordinary English. To get these algorithms to produce output on a computer, you will have to translate the pseudocode into a computer language you are familiar with. I used a language called QBASIC, a version of the well-known programming language BASIC. The execution time of the programs derived from the algorithms given below will depend on a variety of factors, for example, the number of trials requested and the power of your computer.