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PROBABILITY AND STATISTICAL INFERENCE Ninth Edition

Robert V. Hogg

Elliot A. Tanis

Dale L. Zimmerman

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Library of Congress Cataloging-in-Publication Data Hogg, Robert V.

Probability and Statistical Inference/ Robert V. Hogg, Elliot A. Tanis, Dale Zimmerman. – 9th ed.

p. cm. ISBN 978-0-321-92327-1

1. Mathematical statistics. I. Hogg, Robert V., II. Tanis, Elliot A. III. Title. QA276.H59 2013 519.5–dc23

2011034906

10 9 8 7 6 5 4 3 2 1 EBM 17 16 15 14 13

www.pearsonhighered.com ISBN-10: 0-321-92327-8 ISBN-13: 978-0-321-92327-1

http://www.pearsonhighered.com
Contents Preface v

Prologue vii

1 Probability 1 1.1 Properties of Probability 1

1.2 Methods of Enumeration 11

1.3 Conditional Probability 20

1.4 Independent Events 29

1.5 Bayes’ Theorem 35

2 Discrete Distributions 41 2.1 Random Variables of the Discrete Type 41

2.2 Mathematical Expectation 49

2.3 Special Mathematical Expectations 56

2.4 The Binomial Distribution 65

2.5 The Negative Binomial Distribution 74

2.6 The Poisson Distribution 79

3 Continuous Distributions 87 3.1 Random Variables of the Continuous

Type 87

3.2 The Exponential, Gamma, and Chi-Square Distributions 95

3.3 The Normal Distribution 105

3.4* Additional Models 114

4 Bivariate Distributions 125 4.1 Bivariate Distributions of the Discrete

Type 125