Probability and Random Processess Review

The essentials of probability and random processes required in the text are outlined. In this chapter as well as in succeeding chapters, numerical results illustrate the theoretical results. These results are obtained using three different tools as appropriate to the work at hand: Excel, Matlab and Maple. Starting with set theory, and the axioms of probability we derive basic relations, and the concepts of conditional probabilities and independence. The next section deals with random variables and their distribution and density functions. The discussion is in two parts dealing with discrete and continuous random variables, respectively and covers all of the widely used random variables. The probability generating function for discrete random variables and the Laplace transform for continuous random variables receive particular attention because of their role in the text. In subsequent sections, the discussion of basic probability theory is completed with discussions of joint random variables, transformations of random variables and bounds on probabilistic events. The final half of the chapter deals with the fundamentals of Markov chains and of random processes.