概率论与数理统计英文文献.doc

概率论与数理统计英文文献.doc

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Introductiontoprobabilitytheoryand

mathematicalstatistics

Thetheoryofprobabilityandthemathematicalstatisticarecarriesondeductiveandtheinductionsciencetothestochasticphenomenonstatisticalrule,fromthequantitysideresearchstochasticphenomenonstatisticalregularfoundationmathematicsdiscipline,thetheoryofprobabilityandthemathematicalstatisticmaydivideintothetheoryofprobabilityandthemathematicalstatistictwobranches.Theprobabilityusesforthepossiblesizequantitywhichportraystherandomeventtooccur.Theoryofprobabilitymaincontentincludingclassicalgenerallycomputation,randomvariabledistributionandcharacteristicnumeralandlimittheoremandsoon.ThemathematicalstatisticisoneofmathematicsZhongliandepartmentactuallymostdirectlymostwidespreadbranches,itintroducedanestimate（rectangularmethodestimate,enormousestimate）,theparametersuppositionexamination,thenon-parametersuppositionexamination,thevarianceanalysisandthemultipleregressionanalysis,thefail-safeanalysisandsoontheelementaryknowledgeandtheprinciple,enablethestudenttohaveaprofoundunderstandingtostatisticsprinciplefunction.Throughthiscurriculumstudy,enablesthestudentcomprehensivelytounderstand,tograspthetheoryofprobabilityandthemathematicalstatisticthoughtandthemethod,graspsbasicandthecommonlyusedanalysisandthecomputationalmethod,andcanstudiesinthesolutioneconomyandthemanagementpracticequestionusingthetheoryofprobabilityandthemathematicalstatisticviewpointandthemethod.

Randomphenomenon

Fromrandomphenomenon,inthenatureandreallife,somethingsareinterrelatedandcontinuousdevelopment.Intherelationshipbetweeneachotheranddeveloping,accordingtowhetherthereisacausalrelationship,verydifferentcanbedividedintotwocategories:

oneisdeterministicphenomenon.Thiskindofphenomenonisundercertainconditions,willleadtocertainresults.Forexample,undernormalatmosphericpressure,waterheatedto100degreesCelsius,isboundtoaboil.Thislinkisbelongtotheinevitabilitybetweenthings.Usuallyinnaturalscienceisinterdisciplinarystudiesandknowtheinevitability,seekingthiskindofinevitablephenomenon.Anotherkindisthephenomenonofuncertainty.Thiskindofphenomenonisundercertainconditions,theresultisuncertain.Thesameworkersonthesamemachinetools,forexample,processinganumberofthesamekindofparts,theyarethesizeofthetherewillalwaysbealittledifference.Asanotherexample,underthesameconditions,artificialacceleratinggerminationtestofwheatvarieties,eachtreeseedgerminationisalsodifferent,thereisstrengthandsoonerorlater,respectively,andsoon.Whyinthesamesituation,willappearthiskindofuncertainresults?

Thisisbecause,wesay"sameconditions"referstosomeofthemainconditions,inadditiontothesemainconditions,therearemanyminorconditionsandtheaccidentalfactorispeoplecan'tinadvanceonebyonetograsp.Becauseofthis,inthiskindofphenomenon,wecan'tusetheinevitabilityofcauseandeffect,theresultsofindividualphenomenoninadvancetomakesureoftheanswer.Therelationshipbetweenthingsisbelongtoaccidental,thisphenomenoniscalledaccidentalphenomenon,orarandomphenomenon.

Innature,intheproduction,life,randomphenomenonisverycommon,thatistosay,thereisalotofrandomphenomenon.Issuesuchas:

sportslotteryofthewinningNumbers,thesameproductionlineproduction,thelifeofthebulb,etc.,isarandomphenomenon.Sowesay:

randomphenomenonis:

underthesameconditions,manytimesthesametestorsurveythesamephenomenon,theresultsarenotidentical,andunabletoaccuratelypredicttheresultsofthenext.Randomphenomenaintheuncertaintiesoftheresults,itisbecauseofsomeminor,causedbytheaccidentalfactors.

Randomphenomenononthesurface,seemstobemessy,thereisnoregularphenomenon.Butpracticehasprovedthatifthesamekindofalargenumberofrepeatedrandomphenomenon,itsoverallpresentcertainregularity.Alargenumberofsimilarrandomphenomenaofthiskindofregularity,asweobservedincreaseinthenumberofthenumberoftimesandmoreobvious.Flipacoin,forexample,eachthrowisdifficulttojudgeonthatside,butifrepeatedmanytimesoftossthecoin,itwillbemoreandmoreclearlyfindthemupisapproximatelythesamenumber.

Wecallthispresentedbyalargenumberofsimilarrandomphenomenaofcollectiveregularity,iscalledthestatisticalregularity.Probabilitytheoryandmathematicalstatisticsisthestudyofalargenumberofsimilarrandomphenomenastatisticalregularityofthemathematicaldisciplines.

Theemergenceanddevelopmentofprobabilitytheory

Probabilitytheorywascreatedinthe17thcentury,itisbythedevelopmentofinsurancebusiness,butfromthegambler'srequest,isthatmathematiciansthoughtthesourceofprobleminprobabilitytheory.

Asearlyasin1654,therewasagamblermaytiredtothemathematicianPASCALproposesaquestiontroublinghimforalongtime:

"meettwogamblersbettingonanumberofbureau,whowillwinthefirstminningswins,allbetswillbewho.Butwhenoneofthemwinsa（a

howshouldbetspointsmethodisonlyreasonable?

"Whoin1642inventedtheworld'sfirstmechanicaladditionofcomputer.

Threeyearslater,in1657,theDutchfamousastronomy,physics,andamathematicianhuygensistryingtosolvethisproblem,theresultsintoabookconcerningthecalculationofagameofchance,thisistheearliestprobabilitytheoryworks.

Inrecentdecades,withthevigorousdevelopmentofscienceandtechnology,theapplicationofprobabilitytheorytothenationaleconomy,industrialandagriculturalproductionandinterdisciplinaryfield.Manyofappliedmathematics,suchasinformationtheory,gametheory,queuingtheory,cybernetics,etc.,arebasedonthetheoryofprobability.

Probabilitytheoryandmathematicalstatisticsisabranchofmathematics,randomtheysimilardisciplinesarecloselylinked.Butshouldpointoutthatthetheoryofprobabilityandmathematicalstatistics,statisticalmethodsareeachhavetheirowncontaindifferentcontent.

Probabilitytheory,isbasedonalargenumberofsimilarrandomphenomenastatisticalregularity,thepossibilitythataresultofrandomphenomenontomakeanobjectiveandscientificjudgment,thepossibilityofitsoccurrenceforthissizetomakequantitativedescription;Comparethesizeofthesepossibilities,studythecontactbetweenthem,thusformingasetofmathematicaltheoriesandmethods.

Mathematicalstatistics-istheapplicationofprobabilitytheorytostudythephenomenonoflargenumberofrandomregularity;Tothroughthescientificarrangementofanumberofexperiments,thestatisticalmethodgivenstricttheoreticalproof;Anddeterminingvariousmethodsappliedconditionsandreliabilityofthemethod,theformula,theconclusionandlimitations.Wecanfromasetofsamplestodecidewhethercanwithquitelargeprobabilitytoensurethatajudgmentiscorrect,andcancontroltheprobabilityoferror.

-isastatisticalmethodprovidesmethodsareusedinavarietyofspecificissues,itdoesnotpayattentiontothemethodaccordingtothetheory,mathematicalreasoning.

Shouldpointoutthattheprobabilityandstatisticsontheresearchmethodhasitsparticularity,andothermathematicalsubjectofthemaindifferencesare:

First,becausetherandomphenomenastatisticalregularityisacollectiverule,musttopresentinalargenumberofsimilarrandomphenomena,therefore,observation,experiment,researchisthecornerstoneofthesubjectresearchmethodsofprobabilityandstatistics.But,asabranchofmathematics,itstillhasthedefinitionofthisdiscipline,axioms,theorems,thedefinitionsandaxioms,theoremsarederivedfromtherandomruleofnature,butthesedefinitionsandaxioms,theoremsiscertain,thereisnorandomness.

Second,inthestudyofprobabilitystatistics,usingthe"bypartconcludedall"methodsofstatisticalinference.Thisisbecauseittheobjectoftheresearch-therangeofrandomphenomenonisverybig,atthetimeofexperiment,observation,notallmaybeunnecessary.Butbythispartofthedataobtainedfromsomeconclusions,concludedthatthereliabilityoftheconclusiontoallthescope.

Third,therandomnessoftherandomphenomenon,referstotheexperiment,investigationbeforespeaking.Aftertherealresultsforeachtest,itcanonlygettheresultsoftheuncertaintyofacertainresult.Whenwestudythisphenomenon,itshouldbenotedbeforethetestcanfinditselfinherentlawofthisphenomenon.

Thecontentofthetheoryofprobability

Probabilitytheoryasabranchofmathematics,itstudiesthecontentgeneralincludetheprobabilityofrandomevents,theregularityofstatisticalindependenceanddeeperadministrativelevels.

Probabilityisaquantitativeindexofthepossibilityofrandomevents.Inindependentrandomevents,ifaneventfrequencyinallevents,inalargerrangeofstablearoundafixedconstant.Youcanthinktheprobabilityoftheincidenttotheconstant.Foranyeventprobabilityvaluemustbebetween0and1.

Thereisacertaintypeofrandomevents,ithastwocharacteristics:

first,onlyafinitenumberofpossibleresults;Second,theresultsthepossibilityofthesame.Havethecharacteristicsofthetworandomphenomenoncalled"classicalsubscheme".

Intheobjectiveworld,therearealargenumberofrandomphenomena,theresultofarandomphenomenonposesarandomevent.Ifthevariable