Introduction to Probability

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CRC Press, Jul 24, 2014 - Mathematics - 596 pages
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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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Contents

Chapter 1 Probability and counting
1
Chapter 2 Conditional probability
41
Chapter 3 Random variables and their distributions
91
Chapter 4 Expectation
137
Chapter 5 Continuous random variables
195
Chapter 6 Moments
243
Chapter 7 Joint distributions
277
Chapter 8 Transformations
339
Chapter 11 Markov chains
459
Chapter 12 Markov chain Monte Carlo
495
Chapter 13 Poisson processes
519
Appendix A Math
541
Appendix B R
561
Appendix C Table of distributions
567
Bibliography
569
Back Cover
571

Chapter 9 Conditional expectation
383
Chapter 10 Inequalities and limit theorems
421

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About the author (2014)

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

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