Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces.
The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.
Sometime ago I got interested in machine learning. Since machine learning involves a good amount of statistics, I started looking for books or resources on probability. After abandoning two widely recommended books, I chanced upon Blitzstein's lectures, I felt that his book would have much more to offer than the lectures. I found it immensely interesting, the authors provide lucid explanations for every concept. There is a lot of emphasis on building intuition about statistical concepts. To drive these concepts home, the book has a good collection of exercises, for me these were the most exciting part. The problems are carefully crafted and will make you think, merely plugging in the formula won't work. I would heartily recommend this book as a first course in probability.
This book starts from the basic concepts of probability theory and develops it up to the law of large numbers and the central limit theorem (and more). I really like the approach this book takes, with a more intuitive explanation of the concepts rather than just focusing on the mathematics, which often (for me at least) doesn’t provide any idea of *why* these probabilistic results should be true.
The book uses the concept of a “story” to define distributions, which is basically learning by generic example. I find this way more useful than merely stating the density functions, as it becomes a lot easier to recognise when the distributions occur in practice.
The book only relies on basic real analysis, and a tiny bit of linear algebra. As the authors also emphasise: probability isn’t hard mathematics, but what makes it hard is connecting it with the real world and knowing how to apply the vast array of tools available.
5 stars for the effort of giving the intuitive stories for each probability distribution concept.
It does not just introduce the concept but provides many examples of applying probability in real-life situations. Each chapter also has the R codes that connect with the introduced concepts for readers to play around.
Without much exaggeration, this is the single most important book I have read in my life. It introduced me to the possibility of extending logic to the realm of unpredictability and chaos. The abundant amount of concrete and vivid examples helped me to appreciate many of the core concepts of probability and statistics. I sincerely recommend this book to anyone who wants a lucid, fascinating, and at times challenging read.