Probability and Random Processes for Electrical Engineering (2nd Edition) (Paperback)

~ Albert Leon-Garcia (Author)

Editorial Reviews

Product Description

Presents a carefully motivated, accessible, and interesting introduction to probability and random processes. Includes sections on modeling, basic statistical techniques, computer simulation, and reliability. DLC: Electric engineering-Mathematics.

From the Inside Flap

Probability and Random Processes for Electrical Engineering presents a carefully motivated, accessible, and interesting introduction to probability and random processes. It is designed to allow the instructor maximum flexibility in the selection of topics. In addition to the standard topics taught in introductory courses on probability, random variables, and random processes, the book includes sections on modeling, basic statistical techniques, computer simulation, reliability, and entropy, as well as concise but relatively complete introductions to Markov chains and queueing theory.

The complexity of the systems encountered in electrical and computer engineering calls for an understanding of probability concepts and a facility in the use of probability tools from an increasing number of B.S. degree graduates. The introductory Course should therefore teach the student not only the basic theoretical concepts but also how to solve problems that arise in engineering practice. This course requires that the student develop problem-solving skills and understand how to make the transition from a real problem to a probability model for that problem. Relevance to Engineering Practice

Motivating students is a major challenge in introductory probability courses. Instructors need to respond by showing students the relevance of probability theory to engineering practice. Chapter 1 addresses this challenge by discussing the role of probability models in engineering design. Practical applications from various areas of electrical and computer engineering are used to show how averages and relative frequencies provide the proper tools for handling the design of systems that involve randomness. These application areas are used in examples and problems throughout the text. From Problems to Probability Models

The transition from real problems to probability models is shown in several ways. First, important concepts are usually developed by presenting real data or computer-simulated data. Second, sections on basic statistical techniques are integrated throughout the text. These sections demonstrate how statistical methods provide the link between theory and the real world. Finally, the significant random variables and random processes are developed using model-building arguments that range from simple to complex. For example, in Chapter 2 and 3, text discussion proceeds from coin tossing to Bernoulli trials. It then continues to the binomial and geometric distributions, and finally proceeds via limiting arguments to the Poisson, exponential, and Gaussian distributions. Examples and Problems

Numerous examples in every section are used to demonstrate analytical and problem-solving techniques, develop concepts using simplified cases, and illustrate applications. The text includes over 700 problems, identified by section to help the instructor select homework problems. Additional sets of problems requiring cumulative knowledge are provided at the end of each chapter. Answers to selected problems are included at the end of the text. A Student Solutions Manual accompanies this text to develop problem-solving skills. A sampling of 25% of carefully worked out problems has been selected to help students understand concepts presented in the text. An Instructors Solutions Manual with complete solutions is also available. Computer Methods

The development of an intuition for randomness can be aided by the use of computer exercises. Appendix C contains computer programs for generating several well-known random variables. The resulting data from computer-generated random numbers and variables can be analyzed using the statistical methods introduced in the text.

Sections on computer methods have been integrated into the text rather than isolated in a separate chapter because performing the computer exercises during lessons helps students to learn basic probability concepts. It should be noted that the computer methods introduced in Sections 2.7, 3.11, and 4.10 do not necessarily require entirely new lectures. The transformation method in Section 3.11 can be incorporated into the discussion on functions of a random variable. Similarly, the material in Section 4.10 can be incorporated into the discussion on transformations of random vectors. Random Variables and Continuous-Time Random Processes

Discrete-time random processes provide a crucial "bridge" in going from random variables to continuous-time random processes. Care is taken in the first five chapters to lay the proper groundwork for this transition. Thus sequences of dependent experiments are discussed in Chapter 2 as a preview of Markov chains. In Chapter 4, emphasis is placed on how a joint distribution generates a consistent family of marginal distributions. Chapter 5 introduces sequences of independent identically distributed (iid) random variables. Chapter 6 considers the sum of an iid sequence to produce important examples of random processes. Throughout Chapters 6 and 7, a concise development of the concepts is achieved by developing discrete-time and continuous-time results in parallel. Markov Chains and Queueing Theory

Markov chains and queueing theory have become essential tools in communication network and computer system modeling. In the introductory course on probability only a few changes need to be made to accommodate these new requirements. The treatment of conditional probability and conditional expectation needs to be modified, and the Poisson and gamma random variables need to be given greater prominence. In an introductory course on random processes a new balance needs to be struck between the traditional discussion of wide-sense stationary processes and linear systems and the discussion of Markov chains and queueing theory. The "optimum" balance between these two needs will surely vary from instructor to instructor, so the text includes more material than can be covered in one semester in order to give the instructor leeway to strike a balance. Suggested Syllabi

The first five chapters form the basis of a one-semester introduction to probability. In addition to the optional sections on computer methods, these chapters also include optional sections on combinatorics, reliability, confidence intervals, and basic results from renewal theory. In a one-semester course, it is possible to provide an introduction to random processes by omitting all the starred sections in the first five chapters and covering instead the first part of Chapter 6. The material in the first five chapters has been used at the University of Toronto in an introductory junior-level required course for electrical engineers.

A one-semester course on random processes with Markov chains can be taught using Chapters 6 though 8. A quick introduction to Markov chains and queueing theory is possible by covering only the first three sections of Chapter 8 and then proceeding to the first few sections in Chapter 9. A one-semester introduction to queueing theory can be taught from Chapters 6, 8, and 9. Changes in the Second Edition

The only changes in the second edition that affect the first half of the book, and hence introductory courses on probability, involve the addition of more examples and problems. In keeping with our goal of giving the instructor flexibility in the selection of topics, we have expanded the optional section on reliability (Section 3.10) and introduced a new optional section on entropy (Section 3.12). Care has been taken not just to define the various quantities associated with entropy but also to develop an understanding of the interpretation of entropy as a measure of uncertainty and information.

The most significant change to the second edition is the addition of material to make the text more suitable for a course that provides a more substantial introduction to random processes:

In Chapter 4, a section on the joint characteristic function has been added and the discussion of jointly Gaussian random variables has been expanded.

Section 5.5 discusses the various types of convergence of sequences of random variables. A carefully selected set of examples is presented to demonstrate the differences in the various types of convergence.

Section 6.6 uses these results to develop the notions of mean square continuity, derivatives, and integrals of random processes. This section presents the relations between the Wiener process and white Gaussian noise. It also develops the Ornstein-Uhlenbeck process as the transient solution to a first-order linear system driven by noise.

Section 6.8 uses Fourier series to introduce the notion of representing a random process by a linear combination of deterministic functions weighted by random variables. It then proceeds to develop the Karhunen-Loeve expansion for vector random variables and then random processes.

Section 7.4 now contains a separate section on prediction and the Levinson algorithm.

Finally, Section 7.5 presents a discussion of the Kalman filter to complement the Wiener filter introduced in Section 7.4. Acknowledgments

I would

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Product Details

• Paperback: 596 pages
• Publisher: Prentice Hall; 2 edition (August 10, 1993)
• Language: English
• ISBN-10: 020150037X
• ISBN-13: 978-0201500370
• Product Dimensions: 9.5 x 7.8 x 1.1 inches
• Shipping Weight: 2.5 pounds
• Average Customer Review: 2.7 out of 5 stars  See all reviews (27 customer reviews)
• Amazon.com Sales Rank: #624,768 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

14 of 16 people found the following review helpful:

1.0 out of 5 stars Run and Hide, November 13, 2005

By	BUS/ENG grad student "Joe" (New Mexico) - See all my reviews

This review is from: Probability and Random Processes for Electrical Engineering (Paperback)

I intend to burn this book once the semester is over; it is utterly worthless. My professor was coerced to use the book and assigns homework from the book, but the exams look nothing at all like the homework or material from the book.

My complaints:
Insuffucient examples to teach a concept. There is an inextricably, monotonous presence of teaching. The examples are nowhere near adequate to be able to do the problems in the back of the chapter. Superficially, the content looks great, but when you try to learn it from the book, the frustration builds until you cry.

The wording of chapter exercises and end of chapter problems is vague and problemmatic. It is difficult to understand what is being taught, if anything is being taught at all. I would like to use this as a reference when I graduate, but realistically, if it's as useful as cow dung now, then why would I keep it?

So, get it all over with now, the crying, the late nights pulling hair out, seeking antidepressants for the incessant crying and depression due to frustration. Be realistic in the beginning. Unless you have an excellent professor, you will probably not make a good grade based on homework and/or exams from this book. Better yet, don't buy the book - you might get a better grade on the exams if you are exposed to the unnecessary stress.

[This is just an opinion - don't sue me. If, by some strange reason, you're a math major, then you might have a partial background to cope with the book's inadequacies and take a different view.]

7 of 7 people found the following review helpful:

1.0 out of 5 stars Could be done much better than this!, October 27, 2002

By A Customer

If you are in EE, at first glance this book looks perfect. All of the example are on electrical engineering stuff, you see lots of graphs and the book has many tables on the cover making it nice for reference.

However... when you really get into this book, you will quickly realize it is pretty worthless.

For example chapter 3 is over 100 pages long. It is called random variables. In this single chapter they introduce random variables, functions of random variables, expectation of R.V. and functions of R.V., Markov and Chebyshev inequalities as well as Moment generating functions and Characteristic functions, entropy as well as a few others. I hope you are thinking WHEW!! This should have easily been 2 or 3 chapters.

Now to boot, there are 160 end of chapter problems! In the chapter there are 71 examples, BUT only about 20 of them are actually useful. The other 51 examples are strange things like Ex. What does the greek character rho mean? It means an outcome! That is not an example in my book. Meanwhile the end of chapter problems are like Q. Take the Laplace transform of the characteristic function and show that it is a Cauchy R.V. Right... and that is in the book where. Oh yeah, I get it, I am just suppose to be able to piece that together from this amazing book and its 71 examples, whatever.

Now, there is a solution manual available for this book with worked out problems. Guess how many are done in chapter 3? There are 34 worked out problems, and they are all of the easiest problems. Out of those 34 problems, only one of them uses the characteristic function. Yet, there are about 50 problems at the end of the chapter on characteristic functions.

Overall I am very dissapointed in this book. No worthwhile examples and the explainations are very weak at times. Compared to Papoulis this book is perhaps equal. However when you are comparing stinky socks to rotten eggs...

7 of 7 people found the following review helpful:

3.0 out of 5 stars Used in Graduate Class on Probability and Random Processes, March 23, 2000

By A Customer

I used this book for a graduate class in Probaility and Random Processes and we covered every chapter. I gave the book three stars based on other probability books I have used, but compared to other engineering books I would rate it lower.

I feel main problem with the book is the examples not very helpful in solving the 100+ problems that accompany each chapter. Most of the examples were just useless explanations graphs. The book also seems to gloss over some of the important concepts needed to solve the homework problems. The only homework problems that I found useful were the MATLAB examples. I would recommend doing these problems even if they are not assigned.

The book also does a poor job covering applications, especially in the later chapters on random processes. I would have been interested in more signal processing and communications applications, the main reason I took a course on probability and random processes.

As far a background for a person using this book, I would recommend the person be graduate student with a solid math background.