A FIRST COURSE IN PROBABILITY - Lelah Terbiasa

1 A FIRST COURSE IN PROBABILITYThis page intentionally left blank A FIRST COURSE IN PROBABILITYE ighth EditionSheldon RossUniversity of Southern CaliforniaUpper Saddle River, New Jersey 07458 Library of Congress Cataloging-in-Publication DataRoss, Sheldon FIRST COURSE in PROBABILITY / Sheldon Ross. 8th bibliographical references and : 978-0-13-603313-4 ISBN-10: 0-13-603313-X1. Probabilities Textbooks. I. dc222008033720 Editor in Chief, Mathematics and Statistics:Deirdre LynchSenior Project Editor:Rachel S.

2 ReeveAssistant Editor:Christina LepreEditorial Assistant:Dana JonesProject Manager:Robert S. MerenoffAssociate Managing Editor:Bayani Mendoza de LeonSenior Managing Editor:Linda Mihatov BehrensSenior Operations Supervisor:Diane PeiranoMarketing Assistant:Kathleen DeChavezCreative Director:Jayne ConteArt Director/Designer:Bruce KenselaarAV Project Manager:Thomas BenfattiCompositor:Integra Software Services Pvt. Ltd, Pondicherry, IndiaCover Image Credit:Getty Images, Inc. 2010, 2006, 2002, 1998, 1994, 1988,1984, 1976 by Pearson Education, Inc.

3 ,Pearson Prentice HallPearson Education, Saddle River, NJ 07458 All rights reserved. No part of this book may be reproduced, in anyform or by any means, without permission in writing from the Prentice Hall is a trademark of Pearson Education, in the United States of America10987654321 ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-XPearson Education, Ltd.,LondonPearson Education Australia PTY. Limited,SydneyPearson EducationSingapore, Pte. LtdPearson Education North Asia Ltd,Hong KongPearson Education Canada, Ltd.

4 ,TorontoPearson Educaci on de Mexico, de Education Japan,TokyoPearson Education Malaysia, Pte. LtdPearson EducationUpper Saddle River, New JerseyFor RebeccaThis page intentionally left blank ContentsPrefacexi1 Combinatorial Introduction .. The Basic Principle of Counting .. Combinations .. Multinomial Coefficients .. The Number of Integer Solutions of Equations .. 12 Summary .. 16 Theoretical Exercises .. 18 Self-Test Problems and Exercises .. 202 Axioms of Introduction.

5 Axioms of PROBABILITY .. Some Simple Propositions .. Sample Spaces Having Equally Likely PROBABILITY as a Continuous Set Function .. PROBABILITY as a Measure of Belief .. 48 Summary .. 50 Theoretical Exercises .. 54 Self-Test Problems and Exercises .. 563 Conditional PROBABILITY and Introduction .. Conditional Probabilities .. Bayes s Formula .. ( |F) Is a PROBABILITY .. 93 Summary .. 102 Theoretical Exercises .. 110 Self-Test Problems and Exercises .. 1144 Random Random Discrete Random Variables.

6 ExpectedValue .. Expectation of a Function of a Random Variance .. The Bernoulli and Binomial Random Variables .. Properties of Binomial Random Computing the Binomial Distribution Function .. The Poisson Random Computing the Poisson Distribution Function .. Other Discrete PROBABILITY Distributions .. The Geometric Random Variable .. The Negative Binomial Random The Hypergeometric Random Variable .. TheZeta(orZipf) Expected Value of Sums of Random Variables .. Properties of the Cumulative Distribution Function.

7 168 Summary .. 172 Theoretical Exercises .. 179 Self-Test Problems and Exercises .. 1835 Continuous Random Introduction .. Expectation and Variance of Continuous Random The Uniform Random Variable .. Normal Random Variables .. The Normal Approximation to the Binomial Distribution .. Exponential Random Variables .. Hazard Rate Other Continuous Distributions .. TheGammaDistribution .. TheWeibullDistribution .. TheBetaDistribution .. The Distribution of a Function of a Random Variable.

8 219 Summary .. 224 Theoretical Exercises .. 227 Self-Test Problems and Exercises .. 2296 Jointly Distributed Random JointDistributionFunctions .. Independent Random Variables .. Sums of Independent Random Variables .. Identically Distributed Uniform Random Variables .. Gamma Random Variables .. Normal Random Variables .. Poisson and Binomial Random Geometric Random Conditional Distributions: Discrete Case .. Conditional Distributions: Continuous Case .. OrderStatistics .. Joint PROBABILITY Distribution of Functions of Random Variables.

9 Exchangeable Random Variables .. 282 Summary .. 287 Theoretical Exercises .. 291 Self-Test Problems and Exercises .. 293 Contentsix7 Properties of Introduction .. Expectation of Sums of Random Variables .. Obtaining Bounds from Expectationsvia the Probabilistic Method .. The Maximum Minimums Identity .. Moments of the Number of Events that Occur .. Covariance, Variance of Sums, and Correlations .. Conditional Expectation .. Computing Expectations by Computing Probabilities by Conditional Variance.

10 Conditional Expectation and Prediction .. Moment Generating Joint Moment Generating Functions .. Additional Properties of Normal Random Variables .. The Multivariate Normal Distribution .. The Joint Distribution of the Sample Meanand Sample Variance .. General Definition of Expectation .. 369 Summary .. 373 Theoretical Exercises .. 380 Self-Test Problems and Exercises .. 3848 Limit Introduction .. Chebyshev s Inequality and the Weak Law of LargeNumbers .. TheCentralLimitTheorem.