Book 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.
Table of contents
- Preliminaries
- Preface
- Chapter 1 Probability and counting
-
Chapter 2 Conditional probability
- 2.1 The importance of thinking conditionally
- 2.2 Definition and intuition
- 2.3 Bayesâ rule and the law of total probability
- 2.4 Conditional probabilities are probabilities
- 2.5 Independence of events
- 2.6 Coherency of Bayesâ rule
- 2.7 Conditioning as a problem-solving tool
- 2.8 Pitfalls and paradoxes
- 2.9 Recap
- 2.10 R
- 2.11 Exercises
-
Chapter 3 Random variables and their distributions
- 3.1 Random variables
- 3.2 Distributions and probability mass functions
- 3.3 Bernoulli and Binomial
- 3.4 Hypergeometric
- 3.5 Discrete Uniform
- 3.6 Cumulative distribution functions
- 3.7 Functions of random variables
- 3.8 Independence of r.v.s
- 3.9 Connections between Binomial and Hypergeometric
- 3.10 Recap
- 3.11 R
- 3.12 Exercises
-
Chapter 4 Expectation
- 4.1 Definition of expectation
- 4.2 Linearity of expectation
- 4.3 Geometric and Negative Binomial
- 4.4 Indicator r.v.s and the fundamental bridge
- 4.5 Law of the unconscious statistician (LOTUS)
- 4.6 Variance
- 4.7 Poisson
- 4.8 Connections between Poisson and Binomial
- 4.9 *Using probability and expectation to prove existence
- 4.10 Recap
- 4.11 R
- 4.12 Exercises
- Chapter 5 Continuous random variables
- Chapter 6 Moments
- Chapter 7 Joint distributions
- Chapter 8 Transformations
- Chapter 9 Conditional expectation
- Chapter 10 Inequalities and limit theorems
- Chapter 11 Markov chains
- Chapter 12 Markov chain Monte Carlo
- Chapter 13 Poisson processes
- A Math
- B R
- C Table of distributions
- Bibliography
Product information
- Title: Introduction to Probability
- Author(s):
- Release date: September 2015
- Publisher(s): CRC Press
- ISBN: 9781498759762
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