Introduction to Probability

Introduction to Probability

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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 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.
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Product details

  • Book | 596 pages
  • 178 x 254 x 33.02mm | 1,260g
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 11/10/15- EBOOKS CORRECTED; 7/15- All new Cam Ready file - Missed 3rd print- Sent all for 4th printing!; 1 Tables, black and white; 115 Illustrations, black and white
  • 1466575573
  • 9781466575578
  • 281,083

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
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Review quote

"... 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
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About Joseph K. Blitzstein

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

114 ratings
4.54 out of 5 stars
5 70% (80)
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3 10% (11)
2 4% (4)
1 0% (0)
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