TABLE OF CONTENTS In this chapter we introduce the fundamental concepts of probability theory. Indeed, performance analysis is mainly concerned with phenomena which are basically unpredictable: examples are the occurrence of equipment breakdowns, the arrivals of connection requests and their durations. These random phenomena may be well described however, on a statistical basis, by using the tools and methods of probability theory.
We present the notions and properties of random variables, and the major theorems founding the theory. We develop also the properties of the transforms of distribution functions, which appear as essential tools in solving complex probabilistic problems.
Probability theory is mainly built on the concept of random event. The particular outcome of this experiment cannot be predicted, although the set of all possible outcomes is known: any particular outcome will be called a "random event".
The concept of random event is quite natural. Consider the classical example consisting in tossing a die: the outcome is one of the six faces coming up, numbered 1, 2, 6. "I toss the die and 3 comes up" is an event. Each such occurrence is an elementary event. Six different outcomes are possible corresponding to any one of the six faces of the die coming up. Nothing is known about the next outcome, except that it belongs to a certain set, which one is usually able to describe. The set of all the possible outcomes (here, the six...
