Introduction
The probability theory began in the seventeenth century in France when two great French mathematicians, Blaise Pascal and Pierre de Fermat, started a correspondence over the games of chance. Today, the probability theory is a well-established and recognized branch of mathematics with applications in most areas of Science and Engineering.
The Handbook is designed from an introductory course in probability. However, as mentioned in the Preface, we tried to make each chapter as independent as possible from the other chapters. Someone in need of a quick reminder can easily read the part of the book he/she is concerned about without going through an entire set of background material.
The present Handbook contains fourteen chapters, the final two being appendices with more advanced material. The sequence of the chapters in the book is as follows. Chapters 1 and 2 introduce the probability space, sigma algebras, and the probability measure. Chapters 3, 4, and 5 contain a detailed study of random variables. After a general discussion of random variables in Chapter 3, we have chosen to separate the discrete and continuous random variables, which are analyzed separately in Chapters 4 and 5 respectively. In Chapter 6 we discuss methods used to generate random variables. In today's world, where computers are part of any scientific activity, it is very important to know how to simulate a random experiment to find out the expectations one may have about the results of the random ...
