Understanding Probability is a unique and stimulating approach to a first course in probability. The first part of the book demystifies probability and uses many wonderful probability applications from everyday life to help the reader develop a feel for probabilities. The second part, covering a wide range of topics, teaches clearly and simply the basics of probability. This fully revised third edition has been packed with even more exercises and examples and it includes new sections on Bayesian inference, Markov chain Monte-Carlo simulation, hitting probabilities in random walks and Brownian motion, and a new chapter on continuous-time Markov chains with applications. Here you will find all the material taught in an introductory probability course. The first part of the book, with its easy-going style, can be read by anybody with a reasonable background in high school mathematics. The second part of the book requires a basic course in calculus.
Features
Fascinating probability problems (Monty Hall, birthday surprise, lottery winners and more) explained in a way that anyone can understand
The author writes with wit and clarity, explaining mathematics in a unique informal style
This third edition now covers Bayesian inference, Markov chain Monte-Carlo simulation, Brownian motion and more
Table of Contents
Preface
Introduction
Part I. Probability in Action:
1. Probability questions
2. The law of large numbers and simulation
3. Probabilities in everyday life
4. Rare events and lotteries
5. Probability and statistics
6. Chance trees and Bayes' rule
Part II. Essentials of Probability:
7. Foundations of probability theory
8. Conditional probability and Bayes
9. Basic rules for discrete random variables
10. Continuous random variables
11. Jointly distributed random variables
12. Multivariate normal distribution
13. Conditioning by random variables
14. Generating functions
15. Discrete-time Markov chains
16. Continuous-time Markov chains
Appendix
Counting methods and ex
Recommended reading
Answers to odd-numbered problems
Bibliography
Index.