ABSTRACT
Probability theory (Appendix Al)* is a self-consistent logical construction whose basic element (the probability o f an event) is axiomatically defined and cannot be measured. Such an idealization would be useless in engineering or physical applications if no key were available to enter in it. The first idea for such a key is to introduce the experimental statistical frequency of the event (Chapter 7) as an empirical measure of its probability, measure that becomes more and more exact as the size n of the experimental sample increases. However, as it will be shown in Chapter 7 and Appendix A4, there is a proof that when n -► oo the probability of a difference between statistical frequency and probability becomes very small, but not that it vanishes. In other words, the identification of frequency and probability is not rigorously possible, not even in the limit for n -+ oo. Nevertheless, human experience teaches that a phenomenon with probability very close to one is almost certain to take place, while an event whose probability of occurrence is very close
* The theory of probability and random processes is systematically presented in Appendices A1 to A8 where many mathematical proofs are also presented. For the reader’s convenience, throughout the book frequent citations refer to the section of Appendices where more detailed and/or rigorous treatment can be found, or to the relevant equations: these citations are easily recognized from the letter A.
