作者	P.Whittle
出版社
出版时间	2003-01-01

特色：

片断：Theapplicationofprobabilitytheorytogamesofchanceisanobviousone.However,thereareapplicationsinscienceandtechnologywhicharejustascleancut.Asexamples,wecanquotethegeneticmechanismofMendelianinheritance(Sections5.5and9.2),theoperationofatelephoneexchange(Section10.4)orthedecayofradioactivemolecules(Section10.4).Inallthesecasesonecanmakevaluableprogresswithasimplemodel,althoughitisonlyfairtoaddthatadeeperstudywilldemandsomethingmorecomplicated.Ingeneral,thephysicalsciencesprovidearichsourceofinterestingandwell-definedprobabilityproblems:see,forexample,someofthemodelsofstatisticalmechanics(Sections6.3and10.9)andBrownianmotion(Section10.11).Theproblemsgeneratedbythetechnologicalsciencescanbejustasinterestingandnolessfundamental:see,forexample,thediscussionofinfor-mationtheory(Sections16.1-16.3)andofroutinginatelephonenetwork(Section10.8).Inencounteringthe'naturalvariability'ofbiologicalproblemsonerunsintorathermorediffusesituations,butthisvariabilitymakesaprobabilisticapproachallthemoreimperative,andonecanconstructprob-abilisticmodelsof,say,populationgrowth(Sections6.4and10.4)andepi-demics(Section10.7)whichhaveproveduseful.Oneencountersnaturalvariabilityinthehumanformifonetriestoconstructsocialoreconomicmodelsbutagainsuchmodels,inevitablyprobabilistic,proveuseful.See,forexample,thediscussionoftheParetodistributioninSection10.5.Oneofthemostrecentandfascinatingapplicationsofprobabilitytheoryistothefieldofcontrolor.moregenerally,tothatofsequentialdecision-making(Section16.4).Onemight,forexample,bewishingtoholdanaircraftoncourse,despitethefactthatrandomforcesofonesortoranothertendtodivertit,oronemightwishtokeepafactoryinastateofover-allefficientproductiondespitethefactthatsomanyfuturevariables(suchasdemandfortheproduct)mustbeuncertain.Ineithercase,onemustmakeasequenceofdecisions(regardingcourseadjustmentorfactorymanagement)insuchawayastoensureeflicientrunningoveraperiod,orevenoptimalrunning,insomewell-definedsense.Moreover,thesedecisionsmustbetakeninthefaceofanuncertainfuture.Itshouldalsobesaidthatprobabilitytheoryhasitsownflavourandintrinsicstructure,quiteapartfromapplications,asmaybeapparentfromChapters2,3,12,13and14inparticular.Justasformathematicsingeneral,peopleargueabouttheextenttowhichthetheoryisself-generating,ordependentuponapplicationstosuggesttherightdirectionandconcepts.Perhapseitherextremeviewisincorrect;thesearchforaninnerpatternandthesearchforaphysicalpatternarebothpowerfulresearchtools,neitherofthemtobeneglected.2.TheEmpiricalBasisCertainexperimentsarenonreproducibleinthat,whenrepeatedunderstan-dardconditions,theyproducevariableresults.Theclassicexampleisthatofcoin-tossing:thetossbeingtheexperiment,resultingintheobservationofaheadoratail.Totakesomethinglessartificial,onemightbeobservingtheresponseofarattoacertaindrug,observationonanotherrat.constitutingrepetitionoftheexperiment.Howeveruniforminconstitutiontheexperimen-talanimalsmaybe,onewillcertainlyobserveavariableresponse.Thesamevariabilitywouldbefoundin,forexample,lifetimesofelectriclamps,cropyields,thecollisionsofphysicalparticlesorthenumberoftelephonecallsmadeoveragivenlineonagivendayoftheweek.Thisvariabilitycannotalwaysbedismissedas'experimentalerror',whichcouldpresumablybeex-plainedandreduced,butmaybesomethingmorefundamental.Forinstance,thenextejectionofanelectronfromahotmetalfilamentisadefiniteevent,whosetimeisnotpredictableonanyphysicaltheoryyetdeveloped.Probabilitytheorycanberegardedasanattempttoprovideaquantitativebasisforthediscussionofsuchsituations,oratleastforsomeofthem.Onemightdespairofconstructingatheoryforphenomenawhoseessentialqualityisthatofimprecision,butthereisanempiricalobservationwhichgivestheneededstartingpoint.Supposeonetossesacoinrepeatedly,keepingarecordofthenumberofheadsr(n)inthefirstntosses(n=1,2,3,..).Considernowtheproportionofheadsafterntosses:Itisanempiricalfactthatp(n)varieswithnmuchasinFig.1.1,whichisderivedfromagenuinecoin-tossingexperiment.Thevaluesofp(n)showFigure1.1.Agraphoftheproportionsofheadsthrown,p(n),inasequenceofnthrows.fromanactualcoin-tossingexperiment.Notethelogarithmicscaleforn.ThefiguresaretakenfromKerrich(1946),bycourtesyofProfessorKerrichandhispublishers.