The Probability Lifesaver: All the Tools You Need to Understand Chance (Princeton Lifesaver Study Guides)

Este libro es lo que habría deseado tener en mi licenciatura en Estadística. La secuencia de los temas se articula de forma progresiva, pedagógica y con rigor suficiente (σ-álgebras, procesos estocásticos, Teorema del Límite Central, función Gamma, Mínimos Cuadrados...), partiendo de lo primario de la Probabilidad, pasando por los Procesos Estocásticos, hasta llegar a la Inferencia Estadística y los Modelos Lineales. Lo que más me agrada es el enfoque pedagógico de contenido digerible y con pretensión de ser una base para los estudios más avanzados (de posgrado) en estos temas. 10/10.

I'm a data scientist and I do data science "stuff". I needed to dig into some advanced aspects of probability theory for my job. I stumbled on this book, and I'm glad I did. It explains complex probability theory in accessible terms, with a great couple of chapters on random variables (better explanations than many other books). Of course, I can expense books for work, but I was so impressed with this book, I bought a copy for my personal use. Highly recommended.

Good

This book is a long read, however, well worth it. It takes the probability principles which are part of all our lives and explains the basics of how formulae are derived. The book is a great read for people fascinated with the Science of Probability and who want a better understanding of how it affects our lives.

This book is a fantastic *supplement* to 3rd or 4th year undergraduate course in probability and a useful reference for a graduate courses that use probability. I think that needs to be emphasized very clearly. The author states that it's intended to supplement a course in probability not replace it. Further, some of the later chapters are fairly self-contained and it is not necessary to read every single chapter to get a lot out of this book. However, I do think reading this book in its entirety will give you a pretty solid foundation in probability theory. The book covers basically everything you would expect in a standard probability course (basic set theory, combinatorics, counting, probability laws and axioms, independence/dependence, conditional and joint probability, Bayes' theorem, PDFs/CDFs, convolutions, moments, continuous and discrete distribution, limit theorems) and some things that are not in every book (hypothesis testing, difference equations, Markov processes, least squares). In terms of math level, this book is not afraid to delve into these details with a lot of calculus and infinite series/summations. If you have not taken these courses that covered these topics yet then it is possible to still follow through this book but it may not be the right level for you. While the book is very thick, a lot of that is due to the conversational style of writing which makes it a pleasure to read. Many problems are proofs are walked through in great detail with a lot of explanation of what approach to use and even temporarily going down the wrong (but what might initially appear to be correct) path for didactic purposes. In many cases the author even guides the reader by trying to explain how one might even think about the problem and some good approaches to help to develop better strategies and intuitions. I truly appreciated reading this and felt like I learned a lot from this style. Also, check out the YouTube videos on the authors website. These are a very helpful supplement. What makes this book a little unusual is that there is a pretty heavy emphasis on proofs. A good deal of the text tries to teach the reader how to think about proofs, what and what not to try, and the appendices are full of information on proof strategies. If you are trying to learn this stuff very deeply or your teacher emphasizes proofs this could be extremely useful but sometimes this is just not what you need out of a probability textbook. I appreciate how much the author wants us to learn, and learn very well, but it all depends on why you bought this book. Thankfully, these sections can easily be skipped if they are not necessary. Looking at some of the reviews on here already it seems many readers were scared off by the introduction and heavy emphasis on combinatorics and counting early on. I can see how this might happen. The intro to the book and some of the first few chapters are quite frankly absurd for someone who is trying to learn probability. The author is very encouraging and has a lot of confidence in his readers but starting off the first chapter with a ton of summations could be extremely intimidating if this is your first textbook in probability. If you find the intro challenging I would recommend skipping it as well as all chapters on counting for the time being. These are difficult topics even when you have a pretty good grasp on the probability basics. Adding to the above, the author tries quite early on to ground some of probability in real analysis and sigma algebra. The author specifies that these sections can be skipped but if you have never thought about how probability spaces need to be defined, I can see how this might be very intimidating as well. In the end, if you are skipping around a lot it can make the book feel like it is meandering a bit too much. I don't think this is a huge problem as the book is still very comprehensive but it makes me sad to see so many people in the reviews who got scared off. Finally, the Mathematica code is a nice addition but extremely poorly written from a coding perspective. Yes, a lot of this doesn't matter when you are just writing one-off functions but when you are five levels deep in nested for-loops you should consider an alternative strategy. Also, consider that Mathematica is a fantastic language but not particularly popular. Rewriting the code in Python or R might be a good exercise for the reader. In summary, this book is a lot of fun to read, engaging, and comprehensive. However, the chapter organization and side-tracks to other topics may lead to the book being intimidating for some. I recommend just skipping these sections and getting out of the book what you need. It's a great book and I highly recommend it.