Introduction to Probability - 2nd Edition - ISBN: 9780128000410, 9780128001981

Introduction to Probability

2nd Edition

Authors: George Roussas
eBook ISBN: 9780128001981
Hardcover ISBN: 9780128000410
Imprint: Academic Press
Published Date: 2nd December 2013
Page Count: 546
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Description

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.

Key Features

  • 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

Readership

Upper level undergraduate students and graduate level students

Table of Contents

Dedication

Preface

Overview

Chapter Descriptions

Features

Concluding Comments

Preface to the Second Edition

Chapter 1. Some Motivating Examples

Abstract

Chapter 2. Some Fundamental Concepts

Abstract

2.1 Some Fundamental Concepts

2.2 Some Fundamental Results

2.3 Random Variables

2.4 Basic Concepts and Results in Counting

Chapter 3. The Concept of Probability and Basic Results

Abstract

3.1 Definition of Probability

3.2 Some Basic Properties and Results

3.3 Distribution of a Random Variable

Chapter 4. Conditional Probability and Independence

Abstract

4.1 Conditional Probability and Related Results

4.2 Independent Events and Related Results

Chapter 5. Numerical Characteristics of a Random Variable

Abstract

5.1 Expectation, Variance, and Moment-Generating Function of a Random Variable

5.2 Some Probability Inequalities

5.3 Median and Mode of a Random Variable

Chapter 6. Some Special Distributions

Abstract

6.1 Some Special Discrete Distributions

6.2 Some Special Continuous Distributions

Chapter 7. Joint Probability Density Function of Two Random Variables and Related Quantities

Abstract

7.1 Joint d.f. and Joint p.d.f. of Two Random Variables

7.2 Marginal and Conditional p.d.f.’s, Conditional Expectation, and Variance

Chapter 8. Joint Moment-Generating Function, Covariance, and Correlation Coefficient of Two Random Variables

Abstract

8.1 The Joint m.g.f. of Two Random Variables

8.2 Covariance and Correlation Coefficient of Two Random Variables

8.3 Proof of Theorem 1, Some Further Results

Chapter 9. Some Generalizations to k Random Variables, and Three Multivariate Distributions

Abstract

9.1 Joint Distribution of k Random Variables and Related Quantities

9.2 Multinomial Distribution

9.3 Bivariate Normal Distribution

9.4 Multivariate Normal Distribution

Chapter 10. Independence of Random Variables and Some Applications

Abstract

10.1 Independence of Random Variables and Criteria of Independence

10.2 The Reproductive Property of Certain Distributions

10.3 Distribution of the Sample Variance under Normality

Chapter 11. Transformation of Random Variables

Abstract

11.1 Transforming a Single Random Variable

11.2 Transforming Two or More Random Variables

11.3 Linear Transformations

11.4 The Probability Integral Transform

11.5 Order Statistics

Chapter 12. Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results

Abstract

12.1 Convergence in Distribution and in Probability

12.2 The Weak Law of Large Numbers and the Central Limit Theorem

12.3 Further Limit Theorems

Chapter 13. An Overview of Statistical Inference

Abstract

13.1 The Basics of Point Estimation

13.2 The Basics of Interval Estimation

13.3 The Basics of Testing Hypotheses

13.4 The Basics of Regression Analysis

13.5 The Basics of Analysis of Variance

13.6 The Basics of Nonparametric Inference

Appendix 20. Appendix

Chapter 21. Some Notation and Abbreviations

Appendix 22. Answers to Even-Numbered Exercises

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Appendix 23. Revised Answers Manual to Introduction to Probability

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Index

Details

No. of pages:
546
Language:
English
Copyright:
© Academic Press 2014
Published:
Imprint:
Academic Press
eBook ISBN:
9780128001981
Hardcover ISBN:
9780128000410

About the Author

George Roussas

George Roussas

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.

Affiliations and Expertise

University of California, Davis, USA

Reviews

"...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

Ratings and Reviews