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TEST BANK FOR FIRST COURSE IN PROBABILITY BY SHELDON ROSS 9TH EDITION ISBN; 9780321794772
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TEST BANK FOR FIRST COURSE IN PROBABILITY BY SHELDON ROSS 9TH EDITION ISBN; 9780321794772
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,A FIRST COURSE IN PROBABILITYNinth Edition
Sheldon Ross
University of Southern California
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Library of Congress Cataloging-in-Publication Data
Ross, Sheldon M.
A first course in probability / Sheldon Ross, University of Southern California. — Ninth edition.
pages cm
Includes bibliographical references and index.
ISBN 978-0-321-79477-2
1. Probabilities—Textbooks. I. Title.
QA273.R83 2013
519.2—dc23
2012023212
10 9 8 7 6 5 4 3 2 1 EBM 16 15 14 13 12
ISBN-10: 0-321-79477-X
ISBN-13: 978-0-321-79477-2
, Contents
Preface ix Theoretical Exercises 106
1
Self-Test Problems and Exercises 109
Combinatorial Analysis 1
1.1 Introduction 1 4 Random Variables 112
1.2 The Basic Principle of Counting 2 4.1 Random Variables 112
1.3 Permutations 3 4.2 Discrete Random Variables 116
1.4 Combinations 5 4.3 Expected Value 119
1.5 Multinomial Coefficients 9 4.4 Expectation of a Function of a Random
1.6 The Number of Integer Solutions of Variable 121
Equations 12 4.5 Variance 125
Summary 15 4.6 The Bernoulli and Binomial Random
Problems 15 Variables 127
Theoretical Exercises 17 4.7 The Poisson Random Variable 135
Self-Test Problems and Exercises 19 4.8 Other Discrete Probability Distributions 147
2 Axioms of Probability 21
4.9 Expected Value of Sums of Random
Variables 155
2.1 Introduction 21 4.10 Properties of the Cumulative Distribution
Function 159
2.2 Sample Space and Events 21
Summary 162
2.3 Axioms of Probability 25
Problems 163
2.4 Some Simple Propositions 28
Theoretical Exercises 169
2.5 Sample Spaces Having Equally Likely
Outcomes 32 Self-Test Problems and Exercises 173
2.6 Probability as a Continuous Set Function 42
2.7 Probability as a Measure of Belief 46 5 Continuous Random
Summary 47 Variables 176
Problems 48
5.1 Introduction 176
Theoretical Exercises 52
5.2 Expectation and Variance of Continuous
Self-Test Problems and Exercises 54 Random Variables 179
3 Conditional Probability
5.3
5.4
The Uniform Random Variable 184
Normal Random Variables 187
and Independence 56
5.5 Exponential Random Variables 197
3.1 Introduction 56 5.6 Other Continuous Distributions 203
3.2 Conditional Probabilities 56 5.7 The Distribution of a Function
3.3 Bayes’s Formula 62 of a Random Variable 208
3.4 Independent Events 75 Summary 210
3.5 P (·|F ) Is a Probability 89 Problems 212
Summary 97 Theoretical Exercises 214
Problems 97 Self-Test Problems and Exercises 217
vii
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