TABLE OF CONTENTS In this chapter we introduce the fundamental concepts of probability theory. Indeed, telecommunication systems are mainly concerned with basically unpredictable phenomena. In order to analyze a signal, as well as to process information or to characterize the performance and reliability of equipment, the engineer is permanently faced with random phenomena. This explains the need to handle them using the tools and methods of probability theory.
We present the notions and properties of random variables, and the major theorems underpinning the theory. We also develop 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 events. The particular outcome of an 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 a random event is quite natural. Consider the traditional example consisting of tossing a die: the outcome is that one of the six faces will come 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, one which is usually able to be described. The...
