Book description
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 realworld 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.
Table of contents
 Preliminaries
 Preface
 Chapter 1 Probability and counting

Chapter 2 Conditional probability
 2.1 The importance of thinking conditionally
 2.2 Definition and intuition
 2.3 Bayes’ rule and the law of total probability
 2.4 Conditional probabilities are probabilities
 2.5 Independence of events
 2.6 Coherency of Bayes’ rule
 2.7 Conditioning as a problemsolving tool
 2.8 Pitfalls and paradoxes
 2.9 Recap
 2.10 R
 2.11 Exercises

Chapter 3 Random variables and their distributions
 3.1 Random variables
 3.2 Distributions and probability mass functions
 3.3 Bernoulli and Binomial
 3.4 Hypergeometric
 3.5 Discrete Uniform
 3.6 Cumulative distribution functions
 3.7 Functions of random variables
 3.8 Independence of r.v.s
 3.9 Connections between Binomial and Hypergeometric
 3.10 Recap
 3.11 R
 3.12 Exercises

Chapter 4 Expectation
 4.1 Definition of expectation
 4.2 Linearity of expectation
 4.3 Geometric and Negative Binomial
 4.4 Indicator r.v.s and the fundamental bridge
 4.5 Law of the unconscious statistician (LOTUS)
 4.6 Variance
 4.7 Poisson
 4.8 Connections between Poisson and Binomial
 4.9 *Using probability and expectation to prove existence
 4.10 Recap
 4.11 R
 4.12 Exercises
 Chapter 5 Continuous random variables
 Chapter 6 Moments
 Chapter 7 Joint distributions
 Chapter 8 Transformations
 Chapter 9 Conditional expectation
 Chapter 10 Inequalities and limit theorems
 Chapter 11 Markov chains
 Chapter 12 Markov chain Monte Carlo
 Chapter 13 Poisson processes
 A Math
 B R
 C Table of distributions
 Bibliography
Product information
 Title: Introduction to Probability
 Author(s):
 Release date: September 2015
 Publisher(s): CRC Press
 ISBN: 9781498759762
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