概率论及其应用导论第1卷第3版

¡¡¡¡WHENTHISBOOKWASFIRSTCONCEIVED£¨MORETHAN25YEARSAGO£©fewmathematiciansoutsidetheSovietUnionrecognizedprobabilityasalegitimatebranchofmathematics.Applicationswerelimitedinscope£¬andthetreatmentofindividualproblemsoftenledtoincrediblecom-plications.Underthesecircumstancesthebookcouldnotbewrittenforanexistingaudience£¬ortosatisfyconsciousneeds.Thehopewasrathertoattractattentiontolittle-knownaspectsofprobability£¬toforgelinksbetweenvariousparts£¬todevelopunifiedmethods£¬andtopointtopotentialapplications.Becauseofagrowinginterestinprobability£¬thebookfoundunexpectedlymanyusersoutsidemathematicaldisciplines.Itswidespreadusewasuncterstandableaslongasitspointofviewwasnewanditsmaterialwasnototherwiseavailable.Butthepopularityseemstopersistevennow£¬whenthecontentsofmostchaptersareavail-ableinspecializedworksstreamlinedforparticularneeds.Forthisreasonthecharacterofthebookremainsunchangedinthenewedition.Ihopethatitwillcontinuetoserveavarietyofneedsand£¬inparticular£¬thatitwillcontinuetofindreaderswhoreaditmerelyforenjoymentandenlightenment.ThroughouttheyearsIwasthegratefulrecipientofmanycommunica-tionsfromusers£¬andtheseledtovariousimprovements.¡¡¡¡Manysectionswererewrittentofacilitatestudy.ReadingisalsoimprovedbyabettertypefaceandthesuperioreditingjobbyMrs.H.McDougal£ºalthoughaprofessionaleditorshehaspreservedafeelingfortherequirementsofreadersandreason.Thegreatestchangeisinchapter¢ó.Thischapterwasintroducedonlyinthesecondedition£¬whichwasinfactmotivatedprincipallybytheunexpecteddiscoverythatitsenticingmaterialcouldbetreatedbyelementarymethods.Butthistreatmentstilldependedoncombinatorialartificeswhichhavenowbeenreplacedbysimplerandmorenaturalprobabilisticarguments.Inessencethisnewchapterisnew.Mostconspicuousamongotheradditionsarethenewsectionsonbranchingprocesses£¬onMarkovchains£¬andontheDeMoivre-Laplacetheorem.Chapter¢ú¢øhasbeenrearranged£¬andthroughoutthebookthereappearminorchangesaswellasnewexamplesandproblems.Iregretthemisleadingnatureoftheauthorindex£¬butIfeltobligedtostateexplicitlywheneveranideaorexamplecouldbetracedtoapartic-ularsource.Unfortunatelythismeansthatquotationsusuallyrefertoanincidentalremark£¬andarerarelyindicativeofthenatureofthepaperquoted.Furthermore£¬manyexamplesandproblemswereinspiredbyreadingnon-mathematicalpapersinwhichrelatedsituationsaredealtwithbydifferentmethods.(Thatnewertextsnowquotethesenon-mathematicalpapersascontainingmyexamplesshowshowfastprob-abilityhasdeveloped£¬butalsoindicatesthelimitedusefulnessofquotations.£©Lackofspaceaswellasofcompetenceprecludedmoreadequatehistoricalindicationsofhowprobabilityhaschangedfromthesemimysteriousdiscussionsofthetwentiestoitspresentflourishingstate.ForanumberofyearsIhavebeenprivilegedtoworkwithstudentsandyoungercolleaguestowhosehelpandinspirationIowemuch.MuchcreditforthisisduetothesupportbytheU.S.ArmyResearchOfficeforworkinprobabilityatPrincetonUniversity.MyparticularthanksareduetoJayGoldmanforathoughtfulmemorandumabouthisteachingexperiences£¬andtoLorenPittfordevotedhelpwiththeproofs.