Introduction to Probability

Preface
1. Some Motivating Examples
2. Some Fundamental Concepts
3. The Concept of Probability and Basic Results
4. Conditional Probability and Independence
5. Numerical Characteristics of a Random Variable
6. Some Special Distributions
7. Joint Probability Density Function of Two Random Variables and Related Quantities
8. Joint Moment Generating Function, Covariance and Correlation Coefficient of Two Random Variables
9. Some Generalizations to k Random Variables, and Three Multivariate Distributions
10. Independence of Random Variables and Some Applications
11. Transformation of Random Variables
12. Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results
13. An Overview of Statistical Inference
Appendix
Some Notation and Abbreviations
Answers to the Even-Numbered Exercises
Index

George G. Roussas earned a B.S. in Mathematics with honors from the University of Athens, Greece, and a Ph.D. in Statistics from the University of California, Berkeley. As of July 2014, he is a Distinguished Professor Emeritus of Statistics at the University of California, Davis. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes. He is a Fellow of the following professional societies: The American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), The Royal Statistical Society (RSS), the American Association for the Advancement of Science (AAAS), and an Elected Member of the International Statistical Institute (ISI); also, he is a Corresponding Member of the Academy of Athens. Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Throughout his career, Roussas served as Dean, Vice President for Academic Affairs, and Chancellor at two universities; also, he served as an Associate Dean at UC-Davis, helping to transform that institution's statistical unit into one of national and international renown. Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope. He has contributed an obituary to the IMS Bulletin for Professor-Academician David Blackwell of UC-Berkeley, and has been the coordinating editor of an extensive article of contributions for Professor Blackwell, which was published in the Notices of the American Mathematical Society and the Celebratio Mathematica.

"...a very traditional mathematics text on the topic of probability. Readers should be comfortable with multiple integrals and, in spots, a little linear algebra. The writing is clear and concise." --MAA.org, August 18 2014