INTRODUCTION TO PROBABILITY AND STATISTICS FOR …

1 INTRODUCTION TOPROBABILITY AND STATISTICSFOR ENGINEERS AND SCIENTISTSF ifth EditionINTRODUCTION TOPROBABILITY AND STATISTICSFOR ENGINEERS AND SCIENTISTS Fifth Edition Sheldon M. RossUniversity of Southern California, Los Angeles, USAAMSTERDAM BOSTON HEIDELBERG LONDONNEW YORK OXFORD PARIS SAN DIEGOSAN FRANCISCO SINGAPORE SYDNEY TOKYOA cademic Press is an imprint of ElsevierAcademic Press is an imprint of Elsevier32 Jamestown Road, London NW1 7BY, UK525 B Street, Suite 1800, San Diego, CA 92101-4495, USA225 Wyman Street, Waltham, MA 02451, USAThe Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UKFifth Edition 2014 Copyright 2014, 2009, 2004, 1999 Elsevier Inc. All rights part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical,including photocopying, recording, or any information storage and retrieval system, without permission in writing fromthe publisher.

2 Details on how to seek permission, further information about the Publisher s permissions policies and ourarrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can befound at our website: book and the individual contributions contained in it are protected under copyright by the Publisher (other thanas may be noted herein).NoticesKnowledge and best practice in this field are constantly changing. As new research and experience broaden ourunderstanding, changes in research methods or professional practices, may become and researchers must always rely on theirown experience and knowledge in evaluating and usingany information or methods described here in. In using such information or methods they should be mindful oftheir own safety and the safety of others, including parties for whom they have a professional the fullest extent of the law, neither the Publishernor the authors, contributors, or editors, assume anyliability for any injury and/or damage to persons or property as a matter of products liability, negligence orotherwise, or from any use or operation of any methods, products, instructions, or ideas contained in thematerial : 978-0-12-394811-3 Library of Congress Cataloging-in-Publication DataRoss, Sheldon to PROBABILITY and STATISTICS for engineers and scientists / Sheldon M.

3 Ross, Department of IndustrialEngineering and Operations Research, University of California, Berkeley. Fifth 978-0-12-394811-31. Probabilities. 2. Mathematical STATISTICS . I. dc232014011941 British Library Cataloguing in Publication DataA catalogue record for this book is available from the British LibraryFor information on all Academic Press publicationsvisit our web site at and bound in the United States of AmericaForElisePrefaceThe fifth edition of this book continues to demonstrate how to apply PROBABILITY theoryto gain insight into real, everyday statistical problems and situations. As in the previouseditions, carefully developed coverage of PROBABILITY motivates probabilistic models ofreal phenomena and the statistical procedures that follow.

4 This approach ultimatelyresults in an intuitive understanding of statistical procedures and strategies most oftenused by practicing engineers and for students in engineering, computer science, mathematics, STATISTICS , and thenatural sciences. As such it assumes knowledge of elementary AND COVERAGEC hapter 1presents a brief INTRODUCTION to STATISTICS , presenting its two branches of des-criptiveandinferentialstatistics,and ashorthistoryofthesubjectandsomeofthepeo plewhose early work provided a foundation for work done subject matter of descriptive STATISTICS is then considered inChapter tables that describe a data set are presented in this chapter, as are quantities thatare used to summarize certain of the key properties of the data be able to draw conclusions from data, it is necessary to have an understandingof the data s origination.

5 For instance, itis often assumed that the data constitute a random sample from some population. To understand exactly what this means andwhat its consequences are for relating properties of the sample data to properties of theentire population, it is necessary to have some understanding of PROBABILITY , and thatis the subject ofChapter 3. This chapter introduces the idea of a PROBABILITY experi-ment, explains the concept of the PROBABILITY of an event, and presents the axioms study of PROBABILITY is continued inChapter 4, which deals with the importantconcepts of random variables and expectation, and inChapter 5, which considers the binomial, Poisson, hypergeometric, normal, uniform, gamma, chi-square,t,andFare 6, we study the PROBABILITY distribution of such sampling STATISTICS as thesample mean and the sample variance.

6 We show how to use a remarkable theoreticalresult of PROBABILITY , known as the central limit theorem, to approximate the ,wepresentthejointprobabilitydistributio nof the sample mean and the sample variance in the important special case in which theunderlying data come from a normally distributed 7shows how to use data to estimate parameters of interest. For instance, ascientist might be interestedin determining the proportion of Midwestern lakesthat areafflicted by acid rain. Two types of estimators are studied. The first of these estimatesthe quantity of interest with a single number (for instance, it might estimate that47 percent of Midwestern lakes suffer from acid rain), whereas the second providesan estimate in the form of an interval of values (for instance, it might estimate thatbetween 45 and 49 percent of lakes suffer from acid rain).

7 These latter estimators alsotell us the level of confidence we can have in their validity. Thus, for instance, whereaswe can be pretty certain that the exact percentage of afflicted lakes is not 47, it mightvery well be that we can be, say, 95 percent confident that the actual percentage isbetween 45 and 8introduces the important topic of statistical hypothesis testing, which isconcerned with using data to test the plausibility of a specified hypothesis. For instance, ,whichmeasuresthedegreeofplausibilityoft hehypothesisafterthedatahavebeenobserved , tests concerning Bernoulli andPoisson parameters are also 9deals with the important topic of regression. Both simple linearregression including such subtopics as regression to the mean, residual analysis, andweighted least squares and multiple linear regression are 10introduces the analysis of variance.

8 Both one-way and two-way (withand without the possibility of interaction) problems are ,whichcanbeusedtotestwhetheraproposedmod el fit test and apply it to test for independence in contingency tables. The final sectionof this chapter introduces the Kolmogorov Smirnov procedure for testing whetherdata come from a specified continuous PROBABILITY 12deals with nonparametric hypothesis tests, which can be used when oneis unable to suppose that the underlying distribution has some specified parametricform (such as normal).Chapter 13considers the subject matter of quality control, a key statistical tech-nique in manufacturing and production processes. A variety of control charts, includ-ing not only the Shewhart control charts but also more sophisticated ones based onmoving averages and cumulative sums, are 14deals with problems related to life testing.

9 In this chapter, the expo-nential, rather than the normal, distribution plays the key 15, we consider the statistical inference techniques of bootstrap statisti-cal methods and permutation tests. We firstshow how probabilities can be obtained bysimulation and then how to utilize simulation in these statistical inference fifth edition contains a multitude of small changes designed to even furtherincrease the clarity of the text s presentations and arguments. There are also manynew examples and problems. In addition, this edition includes new subsections on The Pareto Distribution (subsection ) Prediction Intervals (subsection ) Dummy Variables for Categorical Data (subsection ) Testing the Equality of Multiple PROBABILITY Distributions (subsection )SUPPLEMENTAL MATERIALSS olutions manual and software useful for solving text examples and problems are avail-able at: thank the following people for their helpful comments on material of the fifthedition: Gideon Weiss, Uniferisty of Haifa N.

10 Balakrishnan, McMaster University Mark Brown, Columbia University Rohitha Goonatilake, Texas A and M University Steve From, University of Nebraska at Omaha Subhash Kochar, Portland State Universityas well as all those reviewers who asked to remain s Manual forINTRODUCTION TOPROBABILITY AND STATISTICSFOR ENGINEERS AND SCIENTISTSF ifth EditionSheldon M. RossDepartment of Industrial Engineeringand Operations ResearchUniversity of California, BerkeleyAMSTERDAM BOSTON HEIDELBERG LONDONNEW YORK OXFORD PARIS SAN DIEGOSAN FRANCISCO SINGAPORE SYDNEY TOKYOA cademic Press is an imprint of ElsevierAcademic Press is an imprint of Elsevier32 Jamestown Road, London NW1 7BY, UK525 B Street, Suite 1800, San Diego, CA 92101-4495, USA225 Wyman Street, Waltham, MA 02451, USAThe Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UKFifth Edition 2014 Copyrightc 2014, 2009, 2004, 1999 Elsevier Inc.