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 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.
The second edition adds many new examples, exercises, and explanations, to deepen understanding of the ideas, clarify subtle concepts, and respond to feedback from many students and readers. New supplementary online resources have been developed, including animations and interactive visualizations, and the book has been updated to dovetail with these resources.
Table of Contents
1. Probability and Counting
2. Conditional Probability
3. Random Variables and Their Distributions
5. Continuous Random Variables
7. Joint Distributions
9. Conditional Expectation
10. Inequalities and Limit Theorems
11. Markov Chains
12. Markov Chain Monte Carlo
13. Poisson Processes
C. Table of Distributions
Joseph K. Blitzstein, Harvard University ,Cambridge, Massachusetts, USA Jessica Hwang, Stanford University, Stanford, California, USA