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# Introduction to Probability: A Free PDF Book by Blitzstein and Hwang

Probability is one of the most important and fascinating branches of mathematics, with applications in almost every field of science, engineering, and social science. If you want to learn more about probability and how it can help you understand the world around you, you might be interested in reading Introduction to Probability, a book by Joseph K. Blitzstein and Jessica Hwang.

In this article, we will give you an overview of what Introduction to Probability is, why you should read it, and how you can access it. We will also answer some frequently asked questions about the book and its authors.

## What is Introduction to Probability?

Introduction to Probability is a textbook that provides an essential language and tools for understanding statistics, randomness, and uncertainty. It is based on the celebrated Harvard statistics lectures by Joseph K. Blitzstein, who is a professor of statistics at Harvard University. The book was co-written by Jessica Hwang, who is an assistant professor of statistics at Stanford University.

### Who are the authors?

Joseph K. Blitzstein is a professor of statistics at Harvard University, where he teaches courses on probability, statistics, machine learning, and data science. He has a PhD in mathematics from Stanford University and a BA in mathematics from Harvard University. He has received several teaching awards, including the Phi Beta Kappa Teaching Prize and the Levenson Prize. He is also the co-director of the Harvard Data Science Initiative.

Jessica Hwang is an assistant professor of statistics at Stanford University, where she teaches courses on probability theory, statistical inference, and Bayesian methods. She has a PhD in statistics from Harvard University and a BS in mathematics from Caltech. She has received several honors and awards, including the Savage Award for best dissertation in Bayesian theory and methods.

### What are the main topics covered?

Introduction to Probability covers a wide range of topics in probability theory, from the basics of counting and combinatorics to advanced topics such as Markov chains, Bayesian inference, and stochastic processes. Some of the main topics covered are:

• The axioms and rules of probability

• Conditional probability and Bayes' rule

• Discrete and continuous random variables

• Expectation, variance, and moments

• Common distributions and their properties

• Joint distributions and independence

• Limits and convergence

• The law of large numbers and the central limit theorem

• Hypothesis testing and confidence intervals

• Monte Carlo simulation and Markov chain Monte Carlo (MCMC)

• Poisson processes and renewal processes

• Markov chains and their applications

• Brownian motion and diffusion processes

## Why should you read Introduction to Probability?

Introduction to Probability is not just another textbook on probability theory. It has several features that make it stand out from other books on the subject. Here are some reasons why you should read Introduction to Probability:

### It provides a comprehensive and rigorous introduction to probability theory

Introduction to Probability covers all the essential topics in probability theory, from the foundations to the frontiers. It does not shy away from mathematical proofs and derivations, but also explains the intuition and motivation behind them. It strikes a balance between theory and practice, and prepares the reader for further study in statistics, machine learning, and data science.

### It explores a wide variety of applications and examples

Introduction to Probability is not just a dry collection of formulas and theorems. It is full of interesting and relevant applications and examples, ranging from coincidences and paradoxes to Google PageRank and cryptography. It shows how probability can be used to model and analyze real-world phenomena, such as genetics, sports, gambling, epidemics, social networks, and more. It also includes historical anecdotes and biographies of famous probabilists and statisticians.

### It includes practice problems and solutions

Introduction to Probability contains over 600 exercises, with varying levels of difficulty and topics. The exercises are designed to test the reader's understanding, reinforce the concepts, and challenge the reader to think creatively and critically. The book also provides detailed solutions to most of the exercises, which can be accessed online at http://probabilitybook.net.

## How can you access Introduction to Probability?

If you are interested in reading Introduction to Probability, you have several options to access it. Here are some of them:

### You can get a free online version of the second edition

The authors have generously made a free online version of the second edition of Introduction to Probability available at http://probabilitybook.net. You can read it online or download it as a PDF file. The online version is updated regularly with corrections and improvements.

### You can buy a print copy from various sources

If you prefer to have a physical copy of Introduction to Probability, you can buy it from various sources, such as CRC Press, Amazon, and elsewhere. The print version is based on the second edition of the book, which was published in 2019 by Chapman & Hall/CRC Press. The print version has some additional features, such as color illustrations, margin notes, and QR codes.

### You can enroll in an edX course based on the book

If you want to learn probability from the authors themselves, you can enroll in an edX course based on Introduction to Probability. The course is called Stat110x: Introduction to Probability, and it is offered by Harvard University. The course focuses on animations, interactive features, readings, and problem-solving. It is complementary to the Stat 110 lecture videos on YouTube, which are available at https://goo.gl/i7njSb. The Stat110x animations are also available at https://goo.gl/g7pqTo.

## Conclusion

In this article, we have given you an overview of what Introduction to Probability is, why you should read it, and how you can access it. We hope that this article has sparked your interest in probability and its applications. If you want to learn more about probability and statistics, we highly recommend reading Introduction to Probability by Joseph K. Blitzstein and Jessica Hwang.

## FAQs

• What is the difference between the first edition and the second edition of Introduction to Probability?

• The second edition of Introduction to Probability has several improvements over the first edition, such as new chapters on Markov chains and stochastic processes, new sections on Bayesian inference and MCMC, more exercises and solutions, more applications and examples, color illustrations, margin notes, QR codes, and more.

• Who is the target audience of Introduction to Probability?

• Introduction to Probability is suitable for anyone who wants to learn probability theory at an undergraduate or graduate level. It can be used as a textbook for a course on probability or as a self-study guide for anyone who wants to learn probability on their own. It assumes that the reader has some background in calculus and linear algebra.

• How long does it take to read Introduction to Probability?

and do all the exercises, it will take you about 20 weeks to finish the book. Of course, you can adjust your pace according to your goals and preferences.

• What are some other books on probability that you recommend?

• There are many other books on probability that you can read, depending on your level and interest. Some of them are:

• A First Course in Probability by Sheldon Ross

• Probability and Random Processes by Geoffrey Grimmett and David Stirzaker

• Probability: Theory and Examples by Rick Durrett

• Probability and Measure by Patrick Billingsley

• The Probability Tutoring Book by Carol Ash

• How can I contact the authors of Introduction to Probability?

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