Introduction to Probability: (Chapman & Hall/CRC Texts in Statistical Science)

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.

Table of Contents:
Probability and Counting Why Study Probability? Sample Spaces and Pebble World Naive Definition of Probability How to Count Story Proofs Non-Naive Definition of Probability Recap R Exercises Conditional Probability The Importance of Thinking Conditionally Definition and Intuition Bayes’ Rule and the Law of Total Probability Conditional Probabilities Are Probabilities Independence of Events Coherency of Bayes’ Rule Conditioning as a Problem-Solving Tool Pitfalls and Paradoxes Recap R Exercises Random Variables and Their Distributions Random Variables Distributions and Probability Mass Functions Bernoulli and Binomial Hypergeometric Discrete Uniform Cumulative Distribution Functions Functions of Random Variables Independence of r.v.s Connections Between Binomial and Hypergeometric Recap R Exercises Expectation Definition of Expectation Linearity of Expectation Geometric and Negative Binomial Indicator r.v.s and the Fundamental Bridge Law of The Unconscious Statistician (LOTUS) Variance Poisson Connections Between Poisson and Binomial Using Probability and Expectation to Prove Existence Recap R Exercises Continuous Random Variables Probability Density Functions Uniform Universality of The Uniform Normal Exponential Poisson Processes Symmetry of i.i.d. Continuous r.v.s Recap R Exercises Moments Summaries of a Distribution Interpreting Moments Sample Moments Moment Generating Functions Generating Moments With MGFs Sums of Independent r.v.s Via MGFs Probability Generating Functions Recap R Exercises Joint Distributions Joint, Marginal, and Conditional 2D LOTUS Covariance and Correlation Multinomial Multivariate Normal Recap R Exercises Transformations Change of Variables Convolutions Beta Gamma Beta-Gamma Connections Order Statistics Recap R Exercises Conditional Expectation Conditional Expectation Given an Event Conditional Expectation Given an r.v. Properties of Conditional Expectation Geometric Interpretation of Conditional Expectation Conditional Variance Adam and Eve Examples Recap R Exercises Inequalities and Limit Theorems Inequalities Law of Large Numbers Central Limit Theorem Chi-Square and Student-t Recap R Exercises Markov Chains Markov Property and Transition Matrix Classification of States Stationary Distribution Reversibility Recap R Exercises Markov Chain Monte Carlo Metropolis-Hastings Gibbs Sampling Recap R Exercises Poisson Processes Poisson Processes in One Dimension Conditioning, Superposition, Thinning Poisson Processes in Multiple Dimensions Recap R Exercises Math Sets Functions Matrices Difference Equations Differential Equations Partial Derivatives Multiple Integrals Sums Pattern Recognition Common Sense and Checking Answers R Vectors Matrices Math Sampling and Simulation Plotting Programming Summary Statistics Distributions Table of Distributions Bibliography Index

About the Author :
Joseph K. Blitzstein, PhD, professor of the practice in statistics, Department of Statistics, Harvard University, Cambridge, Massachusetts, USA

Review :
"… a welcome addition … The authors–wisely, in this reviewer’s opinion–take special care to maintain a conversational tone to prioritize accessibility instead. The result is a very readable text with concepts introduced with a degree of clarity that should suit the beginner extremely well. … An additional feature is the extensive use, and related instruction, of the R programming language for computations, simulations, approximations, and so forth. … beginning students opting for easy-paced learning will find the book highly suited to the purpose … An e-book version of the book is available upon creating an account with the website vitalsource.com and redeeming a code provided with every print copy." —International Statistical Review, 83, 2015 "A few months ago I reviewed Blitzstein and Hwang’s excellent modern Introduction to Probability, which is chock full of features to ease the student’s path. … Blitzstein and Hwang try everything possible to help the student understand the material. … Blitzstein and Hwang have problems with applications to just about anything you can think of … What it comes down to, in my opinion, is that Blitzstein and Hwang is an excellent book for a wide variety of audiences trying to learn probability." —Peter Rabinovitch, MAA Reviews, October 2015 "Introduction to Probability is a very nice text for a calculus-based first course in probability. … The exercises are truly impressive. There are about 600 and some of them are very interesting and new to me. … The website has R code, the previously mentioned solutions, and many videos from the authors teaching the class. The videos are entertaining as well as informative. … In addition to the standard material for such a course, there are also very nicely done chapters on inequalities and limit theorems, Markov chains, and Markov chain Monte Carlo. … this is an excellent text and deserves serious consideration." —MAA Reviews, August 2015 "Unique in its conceptual approach and its incorporation of simulations in R, this book is a welcome addition to the vast collection of probability textbooks currently available. … The topics covered in the book follow a fairly traditional order … The companion website for this textbook, stat110.net, offers supplemental materials to the textbook. There are more than 600 exercises in the textbook, and 250 of these exercises have detailed solutions available on the website. The website offers additional handouts and practice problems and exams, as well as over 30 video lectures available on YouTube or iTunes U. The book is also available as an electronic book. Overall, Introduction to Probability offers a fresh perspective on the traditional probability textbook. Its sections on simulation in R, emphasis on common student mistakes and misconceptions, story-like presentation, and illuminating visualizations provide a comprehensive, well-written textbook that I would consider using in my own probability course." —The American Statistician, August 2015 "Full of real-life motivations and applications, this is a leisurely paced, exercise-laden text, which is also suitable for self-study. Each chapter ends with a Recap section, another section with R code snippets suggesting how to perform calculations and simulations with that program, and finally an Exercises section with an unusually large amount of exercises. Supplementary material is provided ... The book includes a redemption code providing access to an e-book version of the text ..." —Zentralblatt MATH 1300