Introduction to Probability: 1st Edition (e-Book) book cover

Introduction to Probability

1st Edition

By Joseph K. Blitzstein, Jessica Hwang

Chapman and Hall/CRC

596 pages | 115 B/W Illus.

Purchasing Options:$ = USD
Pack - Book and Ebook: 9781466575578
pub: 2014-07-24
SAVE ~$16.05
$107.00
$90.95
x
eBook (VitalSource) : 9781498704786
pub: 2014-08-06
from $49.98


FREE Standard Shipping!

Description

Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and toolsfor 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.

Reviews

"… 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

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 Authors

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

About the Series

Chapman & Hall/CRC Texts in Statistical Science

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General
MAT029010
MATHEMATICS / Probability & Statistics / Bayesian Analysis