Written by one of the founding fathers in this area, the book is filled with illuminating practical examples and (more importantly) ways to think about these types of problems. I used it in grad school and I still use it today in practice. A classic.

This text is for me the best text in the probability/stochastic processes area for engineers and phycisists alike.The explanations are cristal clear,the subject coverage complete and the text organization impeccable.A lot of very instructive examples from communication theory,physics and electrical engineering.I think this book is a must expecially if you want to specialize in communications.Greatly outperforms Papoulis book on the same subject.5 stars!

I have used this book and Vol 2 in my graduate and undergraduate courses. Having used a variety of texts for teaching and learning about probability and statistics in an engineering context, I would say the two volumes by Ang and Tang have no rivals. Lots and lots of good engineering type problems.

We used this text as the first half of a graduate course in engineering reliability. It presented the concepts clearly and in terms of engineering problems rather than card picking and coin flipping like many other probability and statistics texts. It also provided a thorough treatment of the mathematical basis of the sciences of probability and statistics.

The second volume is also an excellent text, though I have had trouble locating it recently. It treats the issues of reliability and decision analysis in more detail.

Stroock in the preface to his preface gives his graduate school introduction to probability from Kac and McKean to explain why the book is written from the analytic rather than the probabilistic viewpoint. The coverage is thorough and rigorous with important proofs provided in the style he likes best. As an example in Chapter 2 where he covers the central limit theorem and the Berry-Esseen results on rates of convergence, he uses Stein's method rather than more complicated approaches using Fourier series.

This covers all the standard topics for a first year graduate course in probability and a bit more.

I am using this book as a reference for a first graduate coursein Probability Theory. In all fairness I must confess that I have notread the whole book, though I have browsed through it and I have read a few pieces here and there. My reason for selecting this book as a reference is partly the fact that the instructor is not using a book, only his notes and this book is listed as an additional reference. Having done some serious book browsing before settling on this one, I can say that its certainly more advanced than typical "first graduate course" books like the ones by Durrett or Williams. The author assumes knowledge of real analysis and launches right away into Probability. The book covers topics like convergence of probability measures and Wiener measure which are given little or no mention in Durrett's and Williams' books. The author in fact devotes an entire chapter to Wiener measure. I don't know if I would like to use this book in isolation. Its pretty advanced and has a whole lot of material that'll take a very long time to read, at least for me. On the other hand, Stroock is a star in the field of Probability and I like his style of writing which is why I did not hesitate to invest a small amount of money (by textbook standards) on an obviously excellent, but difficult reference.

A friend of mine had Carol Ash as his professor for probability theory back in the late '80s and he remembers her quite fondly. Upon looking through the book he told me this a write-up of her lecture notes. Taking probability (a notoriously difficult subject) around the same time I didn't get so lucky. The professor was decent but the book was not and I struggled with probability topics (though curiously enough, I still have it and use it as a reference--time cures all wounds :).

Much later I taught probability and statistics and drew a lot of examples, problems, and explanations for class from this book. It's quite good and very well written, worth your time if you need some extra help understanding your textbook (many of these are shockingly bad) or for self-study. One big selling point is that the problems are quite thoroughly worked out with intermediate steps explained.

Like a good tutor, the "Probability Tutoring Book" explained and clarified points that I'd learned from my instructor and textbook in introductory Probability. Ash's explanations are often very helpful, and her book is loaded with good practice problems. The section on Combinatorics is probably a little too difficult, but I finally managed to grasp the concepts by consulting and doing problems from an old, very helpful book from the library: "Probability: A First Course" by Mosteller, Rourke, and Thomas. Overall, I give Ash's "Probability Tutoring Book" a very high rating as an aid to mastering the fundamentals of probability theory.

This is a truly terrific book covering the basics of probability theory, but it goes far beyond a mere topical treatment of the subject. I was preparing to take a graduate course required for getting a PhD in statistics, and this book was an excellent way to get a leg up in the course. It is clear to me that a great deal of effort and thought was put into making this an excellent text. Thank you Dr. Ash!

As a reliability engineer, I do a lot of probabilistic risk analysis and reliability based design for large systems like gas turbines, etc. From both a theoretical and applied perspective, this is an excellent text for those getting into this subject.

The book is written in a pleasing style, in which complex ideas are introduced in a manner than anyone (with no prior statistical training) can understand. It is a small book that packs a lot of information in it, and the companion volume by the same authors is another excellent text on the same topic. I particularly liked their treatment of LRFD methods and the FORM algorithms.

On the negative side, I found the algorithms described in Madsen's "Methods of structural safety" easier to implement. The authors might want to incorporate some of those methods in their next edition. They could also discuss approaches to model time-dependent reliability, apart from including empirical probability distributions in design.

Overall, I have read most of the texts out there in reliability-based design and this is clearly the best. It's an expensive book, but well worth the money !

This book is among one of the best books in this subject. It captures all different aspects of probability, reliability and statistical methods in engineering design in one book with clear details and examples. The latest advancements in this area are also included in this book. I do recommend it for any engineering student taking courses in this area.

I recommend this book to anyone who is interested in the meaning of statistics. Statistics is based on probability theory, which in turn is dependent on a very specific definition of 'probability'. As such, statistical interpretation should always reflect this definition. This book clarifies the meaning of probability and its impact on statistical reasoning.

It covers the 'grey area' of statistics, too often ignored in university texts.

This book is very easy to read and does not require much exposure to mathematical probability/statistics. The central ideas of the book are applied to 'practical' applications in Physics, which makes it even more interesting.

For the price, it is a great buy!

This outstanding presentation of the frequentist interpretation of probability should be read by all seeking an understanding of what a probability really =is=. One need not accept frequentism (and I do not) to profit greatly from this work.

Ayyub provides an excellent systemic context for the exposition of reliability theory, especially as it relates to applications for decision-makers and decision-making. The mathematical basis of reliability in probability and statisitics is clearly presented and is suitable for engineering students and managers.

In preparing this book, we strove to achieve the following educational objectives: (1) introducing probability, statistics, and reliability methods to engineering students and practicing engineers, (2) emphasizing the practical use of these methods, and (3) establishing the limitations, advantages, and disadvantages of the methods. Although, the book was developed with emphasis on engineering and technological problems, the methods can also be used to solve problems in other fields of sciences.

Problems that are commonly encountered by engineers require decision making under conditions of uncertainty. The uncertainty can be in the definition of a problem, the available information, the alternative solution methodologies and their results, and the random nature of the solution outcomes. Studies show that in the future engineers will need to solve more complex design problems with decisions made under conditions of limited resources, thus necessitating increased reliance on the proper treatment of uncertainty. Therefore, this book is intended to better prepare future engineers, as well as assist practicing engineers, in understanding the fundamentals of probability, statistics, and reliability methods, especially their applications, limitations, and potentials.

STRUCTURE, FORMAT, AND MAIN FEATURES

We have developed this book with a dual use in mind, as both a self-learning guidebook and as a required textbook for a course. In either case, the text has been designed to achieve important educational objectives.

The nine chapters of the book cover of the following subjects: (1) an introduction to the text that covers uncertainty types, decision analysis, and Taylor series expansion; (2) graphical analysis of data, and the computation of important characteristics of sample measurements and basic statistical characteristics; (3) the fundamentals of probability; (4) the joint behavior of random variables and the probabilistic characteristics of functions of random variables; (5) statistical analyses that include parameter estimation, hypothesis testing, confidence-interval estimation, sample-size determination, and probability-model selection; (6) curve fitting or model development based on data using regression analysis; (7) a formal presentation of Monte Carlo simulation; (8) reliability, risk, and decision analysis; and (9) the use of Bayesian methods in engineering. The book was designed for an introductory course in probability, statistics, and reliability with emphasis on applications. In developing the book, a set of educational outcomes as detailed in Chapter 1 motivated the structure and content of this text. Ultimately, serious readers will find the content of the book to be very useful in engineering problem solving and decision making. One of the most difficult to grasp aspects of probability and statistics is the concept of sampling variation. In engineering practice, an engineer typically has only one sample of data. It is important to recognize that the statistical results would be somewhat different if he or she had collected a different sample, even if that sample were equally likely to have occurred. Simulation is a means of demonstrating the sample-to-sample, or sampling, variation that can be expected. For this reason, we have incorporated a section on simulation at the end of each chapter (Chapters 1 to 6). Performing some simulations is one way of generating a better appreciation for sampling variation that is inherent in statistical problems presented in Chapters 1 to 6. Omitting the sections on simulation does not diminish a reader's understanding of the other sections or chapters. In each chapter of the book, computational examples are given in the individual sections of the chapter, with more detailed engineering applications given in a concluding section. Also, each chapter includes a set of exercise problems that cover the materials of the chapter. The problems were carefully designed to meet the needs of instructors in assigning homework and the readers in practicing the fundamental concepts. The book can be covered in one or two semesters depending the level of a course or the time allocated for topics covered in the book. The chapter sequence can be followed as a recommended sequence. However, if needed, instructors can choose a subset of the chapters for courses that do not permit a complete coverage of all chapters or a coverage that cannot follow the presented order. After completing Chapters 1, 2, and 3, the readers will have sufficient background to follow and understand the materials in the following tracks of chapters: Chapter 4; Chapters 5 and 6; Chapters 7 and 8; and Chapter 9 according to the indicated sequence.

Sveshnikov gives a very brief introduction to each topic, with definitions and formulae presented without proofs, followed by a couple of worked examples, and a couple pages of problems. Answers to all problems are in the back, making it ideal for self-study.
If you have not studied any statistics before, you might want to start with a book that gives more explanation, such as Bulmer, "Principles of Statistics."
This book makes use of calculus in many sections. For interesting probability problems with less advanced math, you might try Mosteller, "Fifty Challenging Problems in Probability."
If you take the time to work through a number of problems from each chapter, you can learn how to apply probability and statistics to a wide variety of problems. The equations I derived for the thesis I'm working on are the topic of chapter 6!

Instructors and students alike will find here a real treasure of exercises in probability and statistics. A broad range of topics is covered. Solutions for typical examples are provided at the start of each section. Apart from the more than 1000 problems (the answers and solutions to all of which are provided at the back), the book contains problems both simple and challenging. I personally found some of the latter most fascinating.

This is one of the best books around for studying Random Processes ! The author has also provided a very good introduction to Detection, Estimation and Modelling of Stochastic Processes. I found this book very useful and I'd strongly suggest this book for an introductionary level graduate course. If you want to build a strong foundation in Random Signal Theory, this book is the way to go.. Other advanced texts like Simon Haykin's "Adaptive Filter Theory" will be a lot easier to understand once you study this book thoroughly and work out the exercise problems.

The authors have unleashed the subject of Stochastic Processes using a carefully paced and proven approach of introducing the material using a number of elegant examples where emphasis is to generalize specific results. This quality text will certainly not dissapoint readers who have come to expect high quality from K. Sam Shanmugam and Authur .M.Breipohl .It can be recommended for first course and also for gaduate level courses on the fascinating and challenging subject of Random Processes

The book brings together two of my passions : random
walks and electric networks. It turns out that there are
interesting relationships between these two areas, so insights
in one can be used to prove things in the other.

There is this beautiful theorem by Polya which states that a
random walker on an infinite street network in d-dimensional
space is bound to return to the starting point when d = 2,
but has a positive probability of escaping to infinity without
returning to the starting point when d >= 3. The book
reinterprets this theorem as a statement about electric networks,
and then proves the theorem using techniques from classical
network theory. The proof relies on showing that the resistance
of the corresponding electric network in 1 and 2 dimensions
is infinite, whereas it is finite in the 3 dimensional case.
Thus some current [like our random walker] can flow to infinity.

Strongly recommended!.

This book provides fascinating insights and analogies between random walks and electric networks- and how you can exploit these analogies to solve difficult problems in one using the other... there's also a nice proof of the "Polya's theorem" using these analogies- basically Polya's theorem says that a random walk in dimensions >2 is transient, while a random walk on a plane or a line always returns to its starting point...