Introduction to Probability 2nd Edition by Joseph Blitzstein, Jessica Hwang 1138369918 9781138369917

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ISBN 10: 1138369918

ISBN 13: 9781138369917

Author: Joseph K. Blitzstein, Jessica Hwang

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 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.

Introduction to Probability 2nd Table of contents:

1 Probability and counting

1.1 Why study probability?

1.2 Sample spaces and Pebble World

1.3 Naive definition of probability

1.4 How to count

1.5 Story proofs

1.6 Non-naive definition of probability

1.7 Recap

1.8 R

1.9 Exercises

2 Conditional probability

2.1 The importance of thinking conditionally

2.2 Definition and intuition

2.3 Bayes’ rule and the law of total probability

2.4 Conditional probabilities are probabilities

2.5 Independence of events

2.6 Coherency of Bayes’ rule

2.7 Conditioning as a problem-solving tool

2.8 Pitfalls and paradoxes

2.9 Recap

2.10 R

2.11 Exercises

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

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

5 Continuous random variables

5.1 Probability density functions

5.2 Uniform

5.3 Universality of the Uniform

5.4 Normal

5.5 Exponential

5.6 Poisson processes

5.7 Symmetry of i.i.d. continuous r.v.s

5.8 Recap

5.9 R

5.10 Exercises

6 Moments

6.1 Summaries of a distribution

6.2 Interpreting moments

6.3 Sample moments

6.4 Moment generating functions

6.5 Generating moments with MGFs

6.6 Sums of independent r.v.s via MGFs

6.7 *Probability generating functions

6.8 Recap

6.9 R

6.10 Exercises

7 Joint distributions

7.1 Joint, marginal, and conditional

7.2 2D LOTUS

7.3 Covariance and correlation

7.4 Multinomial

7.5 Multivariate Normal

7.6 Recap

7.7 R

7.8 Exercises

8 Transformations

8.1 Change of variables

8.2 Convolutions

8.3 Beta

8.4 Gamma

8.5 Beta-Gamma connections

8.6 Order statistics

8.7 Recap

8.8 R

8.9 Exercises

9 Conditional expectation

9.1 Conditional expectation given an event

9.2 Conditional expectation given an r.v.

9.3 Properties of conditional expectation

9.4 *Geometric interpretation of conditional expectation

9.5 Conditional variance

9.6 Adam and Eve examples

9.7 Recap

9.8 R

9.9 Exercises

10 Inequalities and limit theorems

10.1 Inequalities

10.2 Law of large numbers

10.3 Central limit theorem

10.4 Chi-Square and Student-t

10.5 Recap

10.6 R

10.7 Exercises

11 Markov chains

11.1 Markov property and transition matrix

11.2 Classification of states

11.3 Stationary distribution

11.4 Reversibility

11.5 Recap

11.6 R

11.7 Exercises

12 Markov chain Monte Carlo

12.1 Metropolis-Hastings

12.2 Gibbs sampling

12.3 Recap

12.4 R

12.5 Exercises

13 Poisson processes

13.1 Poisson processes in one dimension

13.2 Conditioning, superposition, and thinning

13.3 Poisson processes in multiple dimensions

13.4 Recap

13.5 R

13.6 Exercises

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