An Introduction to Probability and Statistical Inference

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.

• 1. Some Motivating Examples and Some Fundamental Concepts2. The Concept of Probability and Some Basic Results3. Numerical Characteristics of a Random Variable, Some Special Random Variables4. Joint and Conditional p.d.f.'s, Conditional Expectation and Variance, Moment Generating Function, Covariance and Correlation Coefficient5. Independence of Random Variables and Some Applications6. Transformation of Random Variables7. Some Modes of Convergence of Random Variables, Applications8. An Overview of Statistical Inference9. Point Estimation10. Confidence Intervals and Confidence Regions11. Testing Hypotheses12. More About Testing Hypotheses13. A Simple Linear Regression Model14. Two Models of Analysis of Variance15. Some Topics in Nonparametric Inference16. Appendix

"The present book is an introductory textbook in probability and statistical inference with a year of calculus and basics of linear algebra as the only prerequisites…. Occasionally, the reader is referred to the above-mentioned textbook for proofs and more comprehensive treatment of some topics. As the author states, the first 7 chapters can be used independently for an introductory probability course." --Andreas N. Philippou, zbMATHOpen