Fundamentals of Applied Probability and Random Processes, Second Edition + Solution manual
Many systems encountered in science and engineering require an understandingof probability concepts because they possess random variations. These include messages arriving at a switchboard; customers arriving at a restaurant, movie theatre or a bank; component failure in a system; traffic arrival at a junction; and transaction requests arriving at a server.
There are several books on probability and random processes. These books range widely in their coverage and depth. At one extreme are the very rigorous books that present probability from the point of view of measure theory and spend so much time proving exotic theorems. At the other extreme are books that combine probability with statistics without devoting enough time on the applications of probability. In the middle lies a group of books that combine probability and random processes. These books avoid the measure theoretic approach and rather emphasize the axioms upon which the theory is based. This book belongs to this group and is based on the premise that to the engineer, probability is a modeling tool. Therefore, to an engineering student the emphasis on a probability and random processes course should be on the application of probability to the solution of engineering problems. Also, since some of the engineering problems deal with data analysis, the student should also be exposed to some knowledge of statistics. However, it is not necessary for the student to take a separate class on statistics since most of the prerequisites for statistics are covered in a probability course. Thus, this book differs from other books in the sense that it presents two chapters on the essentials of statistics.
The book is designed for juniors and seniors, but can also be used at lower graduate levels. It grew out of the author’s fifteen years experience developing and analyzing probabilistic models of systems in the industry as well as teaching an introductory course on probability and random processes for over ten years in two different colleges. The emphasis throughout the book is on the applications of probability, which are demonstrated through several examples that deal with real systems. Sincemany students learn by “doing,” it is suggested that the students solve the exercises at the end of each chapter. Some mathematical knowledge is assumed, especially freshman calculus and algebra.
This second edition of the book differs from the first edition in a few ways. First, the chapters have been slightly rearranged. Specifically, statistics now comes before random processes to enable students understand the basic principles of probability and statistics before studying random processes. Second, Chapter 11 has been split into two chapters: Chapter 8, which deals with descriptive statistics; and Chapter 9, which deals with inferential statistics. Third, the new edition includes more application-oriented examples to enable students to appreciate the application of probability and random processes in science, engineering and management. Finally, after teaching the subject every semester for the past eleven years, I have been able to identify several pain points that hinder student understanding of probability and random processes, and I have introduced several new “smart” methods of solving the problems to help ease the pain.
The book is divided into three parts as follows:
Part 1: Probability and Random Variables, which covers chapters 1 to 7
Part 2: Introduction to Statistics, which covers chapters 8 and 9
Part 3: Basic Random Processes, which covers chapters 10 to 12
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