TLFeBOOK FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS T.T. Soong State University of NewYork at Buffalo, Buffalo, NewYork, USA TLFeBOOK TLFeBOOK FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS TLFeBOOK TLFeBOOK FUNDAMENTALS OF PROBABILITY AND STATISTICS FOR ENGINEERS T.T. Soong State University of NewYork at Buffalo, Buffalo, NewYork, USA TLFeBOOK Copyright2004 JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester, West SussexPO198SQ,England Telephone ( 44)1243779777 Email(for ordersandcustomer serviceenquiries):[email protected] Visit ourHomePageonwww.wileyeurope.comorwww.wiley.com AllRightsReserved.Nopart ofthispublicationmaybereproduced,storedin aretrieval systemortransmitted in anyformorbyanymeans,electronic,mechanical,photocopying, recording,scanningorotherwise,except underthetermsoftheCopyright,Designsand PatentsAct 1988orunderthetermsofalicenceissued bytheCopyright LicensingAgency Ltd,90TottenhamCourtRoad,LondonW1T4LP,UK,withoutthepermissioninwritingof thePublisher.RequeststothePublishershouldbeaddressedtothePermissionsDepartment, John Wiley&SonsLtd,TheAtrium,Southern Gate,Chichester,WestSussexPO198SQ, England,oremailed [email protected],orfaxedto( 44)1243770620. Thispublication isdesignedtoprovideaccurateandauthoritativeinformation inregardto thesubjectmattercovered.ItissoldontheunderstandingthatthePublisherisnotengagedin renderingprofessionalservices.Ifprofessionaladviceorother expert assistanceisrequired, theservicesofacompetent professionalshould besought. OtherWiley EditorialOffices John Wiley&SonsInc.,111River Street,Hoboken,NJ07030,USA Jossey-Bass,989MarketStreet,San Francisco,CA94103-1741,USA Wiley-VCH VerlagGmbH,Boschstr.12,D-69469Weinheim,Germany John Wiley&SonsAustralia Ltd,33ParkRoad,Milton,Queensland 4064,Australia John Wiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,JinXingDistripark, Singapore129809 JohnWiley&SonsCanadaLtd,22WorcesterRoad,Etobicoke,Ontario,CanadaM9W1L1 Wileyalsopublishesitsbooksin avarietyofelectronicformats.Somecontent that appears in print maynot beavailablein electronicbooks. BritishLibrary CataloguinginPublicationData Acataloguerecord for thisbookisavailablefromtheBritish Library ISBN 0-470-86813-9(Cloth) ISBN 0-470-86814-7(Paper) Typesetin 10/12pt TimesfromLaTeXfilessuppliedbytheauthor,processed by Integra SoftwareServices,Pvt.Ltd,Pondicherry,India Printed andboundin Great Britain byBiddlesLtd,Guildford,Surrey Thisbook isprintedonacid-freepaperresponsiblymanufactured fromsustainableforestry inwhich atleast two treesareplantedfor each oneusedfor paperproduction. TLFeBOOK To thememory ofmy parents TLFeBOOK TLFeBOOK Contents PREFACE xiii 1 INTRODUCTION 1 1.1 Organization ofText 2 1.2 Probability Tables and Computer Software 3 1.3 Prerequisites 3 PART A: PROBABILITY AND RANDOM VARIABLES 5 2 BASIC PROBABILITYCONCEPTS 7 2.1 Elements of Set Theory 8 2.1.1 Set Operations 9 2.2 SampleSpaceand Probability Measure 12 2.2.1 Axiomsof Probability 13 2.2.2 Assignment of Probability 16 2.3 Statistical Independence 17 2.4 Conditional Probability 20 Reference 28 Further Reading 28 Problems 28 3 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 37 3.1 Random Variables 37 3.2 Probability Distributions 39 3.2.1 Probability Distribution Function 39 3.2.2 Probability MassFunction for DiscreteRandom Variables 41 TLFeBOOK