Introduction to Probability, Second Edition: 2nd Edition (Hardback) book cover

Introduction to Probability, Second Edition

2nd Edition

By Joseph K. Blitzstein, Jessica Hwang

Chapman and Hall/CRC

620 pages

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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 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.

The second edition adds many new examples, exercises, and explanations, to deepen understanding of the ideas, clarify subtle concepts, and respond to feedback from many students and readers. New supplementary online resources have been developed, including animations and interactive visualizations, and the book has been updated to dovetail with these resources. 

Supplementary material is available on Joseph Blitzstein’s website www. stat110.net. The supplements include:

Solutions to selected exercises

Additional practice problems

Handouts including review material and sample exams Animations and interactive visualizations created in connection with the edX online version of Stat 110.

Links to lecture videos available on ITunes U and YouTube There is also a complete instructor's solutions manual available to instructors who require the book for a course.

Table of Contents

  1. Probability and Counting
  2. 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

  3. Conditional Probability
  4. 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

  5. Random Variables and Their Distributions
  6. Random variables

    Distributions and probability mass functions

    Bernoulli and Binomial

    Hypergeometric

    Discrete Uniform

    Cumulative distribution functions

    Functions of random variables

    Independence of rvs

    Connections between Binomial and Hypergeometric

    Recap

    R

    Exercises

  7. Expectation
  8. Definition of expectation

    Linearity of expectation

    Geometric and Negative Binomial

    Indicator rvs 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

  9. Continuous Random Variables
  10. Probability density functions

    Uniform

    Universality of the Uniform

    Normal

    Exponential

    Poisson processes

    Symmetry of iid continuous rvs

    Recap

    R

    Exercises

  11. Moments
  12. Summaries of a distribution

    Interpreting moments

    Sample moments

    Moment generating functions

    Generating moments with MGFs

    Sums of independent rvs via MGFs

    *Probability generating functions

    Recap

    R

    Exercises

  13. Joint Distributions
  14. Joint, marginal, and conditional

    D LOTUS

    Covariance and correlation

    Multinomial

    Multivariate Normal

    Recap

    R

    Exercises

  15. Transformations
  16. Change of variables

    Convolutions

    Beta

    Gamma

    Beta-Gamma connections

    Order statistics

    Recap

    R

    Exercises

  17. Conditional Expectation
  18. Conditional expectation given an event

    Conditional expectation given an rv

    Properties of conditional expectation

    *Geometric interpretation of conditional expectation

    Conditional variance

    Adam and Eve examples

    Recap

    R

    Exercises

  19. Inequalities and Limit Theorems
  20. Inequalities

    Law of large numbers

    Central limit theorem

    Chi-Square and Student-t

    Recap

    R

    Exercises

  21. Markov Chains
  22. Markov property and transition matrix

    Classification of states

    Stationary distribution

    Reversibility

    Recap

    R

    Exercises

  23. Markov Chain Monte Carlo
  24. Metropolis-Hastings

    Recap

    R

    Exercises

  25. Poisson Processes

Poisson processes in one dimension

Conditioning, superposition, thinning

Poisson processes in multiple dimensions

Recap

R

Exercises

A Math

A Sets

A Functions

A Matrices

A Difference equations

A Differential equations

A Partial derivatives

A Multiple integrals

A Sums

A Pattern recognition

A Common sense and checking answers

B R

B Vectors

B Matrices

B Math

B Sampling and simulation

B Plotting

B Programming

B Summary statistics

B Distributions

C 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

Jessica Hwang is a graduate student in the Stanford statistics department.

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