This one-semester basic probability textbook is written for students in mathematics, physics, engineering, statistics, actuarial science, operations research, and computer science with a background in elementary calculus taking upper level or graduate level introduction to probability courses.
Preface1. Some Motivating Examples2. Some Fundamental Concepts 3. The Concept of Probability and Basic Results4. Conditional Probability and Independence5. Numerical Characteristics of a Random Variable 6. Some Special Distributions7. 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 AppendixSome Notation and Abbreviations Answers to the Even-Numbered ExercisesIndex
George G. Roussas received his B.A. in Mathematics at the University of Athens, Greece, and his Ph.D. in Statistics at the University of California, Berkeley. Roussas is currently Professor and Associate Dean of Statistics at the University of California, Davis. His teaching career began at the University of Wisconsin, Madison. Then he was a Professor of Applied Mathematics at the University of Patras, Greece, and also served as the Dean of the College of Sciences and as Chancellor of that University. At the University of Crete, Greece, Roussas served as Vice President of Academic Affairs. Roussas has published several books, and had more than 65 research papers published in refereed journals. He is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the Royal Statistical Society, and is an elected member of the International Statistical Institute. Finally, Roussas is the Associate Editor of two journals, Statistics and Probability Letters, and Nonparametric Statistics.
"...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
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