Introduction to Probability.

Appendix C Simulation

The whole essence of probability is randomness. Of course uncertainty, and therefore randomness, is omnipresent in nature including all sorts of human activities. However, in the study of natural phenomena and human activities, it is often very useful to be able to produce randomness at a lab or, nowadays, at work or even at home using a personal computer. This is achieved by simulation. Byron Morgan writes in the preface of his book Elements of Simulation (1984) “The use of simulation in statistics dates from the start of the 20th century, coinciding with the beginnings of radio broadcasting and the advent of television. Just as radio and television are now commonplace in our everyday lives, simulation methods are now widely used throughout the many branches of statistics…” Moreover, the use and applications of simulation (not only in probability and statistics) have exploded in recent decades primarily due to the ever growing capability of modern computers. In brief, simulation offers a source of randomness by imitating the realization of a random experiment, such as the throw of a die or the future growth of a company's sales. However, one has to bear in mind that computers are unable to produce truly random realizations, so that computer results are essentially deterministic but they possess the properties of the model we have developed for a random experiment.

A simple such model can be a probability distribution that is used to mimic a real ...