Introduction To Probability 2nd Edition

Excellent book on probability.

The book is an exceptional resource for students across various fields, particularly those studying Artificial Intelligence (AI). It effectively demystifies the complexities of probability theory, making it accessible and engaging for readers at all levels. Learning how to calculate the probability of an event is just the beginning; the book guides you through fundamental concepts, including random variables, expectation, and various probability distributions, with clarity and precision.What sets this book apart is its blend of rigorous theoretical framework with practical examples and exercises that reinforce the material. Bertsekas has a unique ability to present intricate topics in a straightforward manner, which not only aids in comprehension but also sparks interest in the subject.For students pursuing AI, this book serves as an essential foundation, as probability theory is a cornerstone of many AI algorithms and models. The book's well-structured approach makes it a valuable reference for both coursework and self-study, providing the necessary tools to understand and apply probabilistic methods in AI.Overall, 'Introduction to Probability' is a must-have for anyone serious about mastering the concepts and applications of probability. It’s not just a textbook; it’s a comprehensive learning tool that prepares you to tackle real-world problems with confidence, especially in the field of AI.

This book did really save me lots of trouble during my Master's in CS. I've come from a background where we studied calculus and linear algebra but no probability and had to start with courses that assumed a first course in probability and statistics. These types of mathematics books are not usually my favorite as I prefer to go for more rigorous treatments but since I was pressed for time I decided to go with this one instead and less than two months later when I'd barely reached the half-way point I felt like everything in my CS courses are beginning to make sense to me. It absolutely did magic if I must say. I certainly recommend this to anyone who wants a very standard and intuitive treatment of probably and statistics. Although I have to add that this is a book that is more appropriate for students of engineering and hard sciences, students of mathematics would probably need a book where these topics are treated from a measure-theoretic point of view.

If you want to learn probability outside of a physical classroom, this book is an excellent choice. Detailed solutions for all end of chapter problems are available for free from the publisher's website. In addition, this book is used for MIT course 6.041, and MIT offers Open Courseware materials on their website for free. This includes videos of the lectures, as well as more solved problems (beyond those in the book itself) in the form of recitations, problem sets, tutorial problems, and past exams from the MIT class.There is also an edX MOOC that uses this book, with a different set of lectures that are less abbreviated than those for the MIT course.The book itself does a good job of presenting many of the classic problems of probability, including the Monty Hall Problem, the Prisoner's Dilemma, the Two Envelopes Paradox, and the St. Petersburg Paradox. Also, since this is used in the MIT electrical engineering and computer science department, there are problems throughout the book relating to subjects such as reliability and signal degradation.Finally, even though this book covers probability (not probability and statistics), it does cover the normal distribution throughout, as well as the Markov and Chebyshev Inequalities, the Central Limit Theorem, and the Law of Large Numbers. It also contains two chapters added in the 2nd edition covering statistical inference (Classical and Bayesian).

I have used this book and the OCW course for some months now for self study. There are certainly several things to like here:- Consistent and unambiguous notation, few typos, all the mathematics is done very neatly.- Great selection and sequencing of the subjects.- Broad coverage, several concepts which are very useful for problem solving but not emphasized by other books enough like conditioning are full developed here.- Lots and lots of examples (perhaps even too many, as it seems to have come at the expense of finding better explanations for things)- Huge number of problems of varying difficulty, including most of the classic ones (Two envelopes, Gamblers ruin, St. Petersburg, Monty Hall, etc.)Where the book falls short is providing a continuous narrative that would spark any kind of interest in the subject. Concepts are often introduced out of the blue sky, a few examples are shown, and the next part of material proceeds. Excellent example is the section on the normal distribution - formula for it is introduced, some example problems are solved, significant time is spent discussing the use of the tabulated distribution (I would prefer a link to Wolfram Alpha, is there anything particularly noble about using a table instead?) and that's about it, there is not enough motivation that would help with recognizing the concepts in real world settings.Throughout the book you do learn to apply the concepts and theorems, probably enough to solve some textbook problems, but there is too little discussion to develop a deeper understanding. History of the subject is almost completely exempt from the book, so are the so called "philosophical" issues (actually as most will admit of crucial importance in practical applications), and the "applied" examples often feel contrived ("random variable X" is said to be a "signal intensity", but there is not much more to it) or simply uninteresting, while so many great elementary yet non-trivial examples are to be found among real applications (in machine learning, probabilistic algorithms, information theory, coding theory, econometrics, ...). Neither connections to other areas of mathematics get much explored. The exception are the end of chapter exercises, where some more interesting examples and concepts appear.I am reading in parallel Hamming's "The Art of Probability", a book that strongly emphasizes everything that this book omits, but to be fair is also nowhere near as throughout or well-organized as this Bertsekas/Tsitsiklis book. It's funny however that Hamming's book, from 1994, is way more informed by the invention of the computer than this book from 2008, including discussion of simulation, coding theory, numerical issues etc. Hamming also derives the Normal distribution starting from a real world problem, and not just presents the formula. I do hope the authors will publish a third edition that keeps the many advantages of this book but addresses those deficiencies. Meanwhile, I do recommend this book, but I also recommend supplementing it with another one that motivates the subject better, like the book by Hamming.