Introduction to Probability and Stochastic Processes with Applications

PREFACE

This text is designed for a first course in the theory of probability and a subsequent course on stochastic processes or stochastic modeling for students in science, engineering, and economics, in particular for students who wish to specialize in probabilistic modeling. The idea of writing this book emerged several years ago, in response to students enrolled in courses that we were teaching who wished to refer to materials and problems covered in the lectures. Thus the edifice and the building blocks of the book have come mainly from our continuously updated and expanded lecture notes over several years.

The text is divided into twelve chapters supplemented by four appendices. The first chapter presents basic concepts of probability such as probability spaces, independent events, conditional probability, and Bayes’ rule. The second chapter discusses the concepts of random variable, distribution function of a random variable, expected value, variance, probability generating functions, moment generating functions, and characteristic functions. In the third and fourth chapters, we present the distributions of discrete and continuous random variables, which are frequently used in the applications. The fifth chapter is devoted to the study of random vectors and their distributions. The sixth chapter presents the concepts of conditional probability and conditional expectation, and an introduction to the study of the multivariate normal distribution is discussed in seventh chapter. ...