# Introduction to Probability, Second Edition

## George G. Roussas

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Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider.

This edition demonstrates the applicability of probability to many human activities with examples and illustrations. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; special distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Law of Large Numbers; the Central Limit Theorem; and statistical inference. Each section provides relevant proofs, followed by exercises and useful hints. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site.

This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences.

• Demonstrates the applicability of probability to many human activities with examples and illustrations
• Discusses probability theory in a mathematically rigorous, yet accessible way
• Each section provides relevant proofs, and is followed by exercises and useful hints
• Answers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site

"synopsis" may belong to another edition of this title.

Book Description:

Features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples

From the Back Cover:

Introduction to Probability, Second Edition, is written for students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics,  physics, and some of the social sciences with a background in a year-long elementary calculus, taking upper level or graduate level introduction to probability courses. Roussas utilizes his trademark clarity and economy of expression to elucidate important concepts of probability, while providing a plethora of useful examples and exercises of real world applications for students to consider.

Key Features

• Includes text, examples, and graphical illustrations-where appropriate-to motivate the reader, and also demonstrate the applicability of probability in a great variety of human activities
• Provides a mathematically relatively rigorous, yet accessible and always within the prescribed prerequisites, discussion of probability theory, important to students of all disciplines cited above
• Each section provides relevant proofs and is followed by exercises and hints, providing useful clues to the solutions
• Answers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site

George G. Roussas is a Distinguished Professor Emeritus (as of July 01, 2012) of Statistics at the University of California, Davis (UC-Davis), and a well-known author of books, research monographs, editor/co-editor of special volumes, and author/co-author of dozens of research articles published in leading journals of the profession. He is a Fellow of the American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), and the Royal Statistical Society (RSS), an Elected Member of the International Statistical Institute (ISI), and 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. He served as an Associate Dean, Dean, Vice President, and Chancellor at three universities, and he has been instrumental in rendering statistics at UC-Davis nationally and internationally 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 Bulletin of  IMS for Professor -Academician David Blackwell of the UC-Berkeley, and he has been the co-ordinating editor of an article of contributions for same, which appeared in the Notices of the American Mathematical Society; it will be republished in Celebratio Matheimatica.

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