概率论与数理统计英文文献

IntroductiontoprobabilitytheoryandmathematicalstatisticsThetheoryofprobabilityandthemathematicalstatisticarecarriesondeductiveandtheinductionsciencetothestochasticphenomenonstatisticalrule,fromthequantitysideresearchstochasticphenomenonstatisticalregularfoundationmathematicsdiscipline,thetheoryofprobabilityandthemathematicalstatisticmaydivideintothetheoryofprobabilityandthemathematicalstatistictwobranches.Theprobabilityusesforthepossiblesizequantitywhichportraystherandomeventtooccur.Theoryofprobabilitymaincontentincludingclassicalgenerallycomputation,randomvariabledistributionandcharacteristicnumeralandlimittheoremandsoon.ThemathematicalstatisticisoneofmathematicsZhongliandepartmentactuallymostdirectlymostwidespreadbranches,itintroducedanestimate(rectangularmethodestimate,enormousestimate),theparametersuppositionexamination,thenon-parametersuppositionexamination,thevarianceanalysisandthemultipleregressionanalysis,thefail-safeanalysisandsoontheelementaryknowledgeandtheprinciple,enablethestudenttohaveaprofoundunderstandingtostatisticsprinciplefunction.Throughthiscurriculumstudy,enablesthestudentcomprehensivelytounderstand,tograspthetheoryofprobabilityandthemathematicalstatisticthoughtandthemethod,graspsbasicandthecommonlyusedanalysisandthecomputationalmethod,andcanstudiesinthesolutioneconomyandthemanagementpracticequestionusingthetheoryofprobabilityandthemathematicalstatisticviewpointandthemethod.RandomphenomenonFromrandomphenomenon,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.TheemergenceanddevelopmentofprobabilitytheoryProbabilitytheorywascreatedinthe17thcentury,itisbythedevelopmentofinsurancebusiness,butfromthegambler'srequest,isthatmathematiciansthoughtthesourceofprobleminprobabilitytheory.Asearlyasin1654,therewasagamblermaytiredtothemathematicianPASCALproposesaquestiontroublinghimforalongtime:"meettwogamblersbettingonanumberofbureau,whowillwinthefirstminningswins,allbetswillbewho.Butwhenoneofthemwinsa(a<m),theotherwonb(b<m)bureau,gamblingaborted.Q: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.ThecontentofthetheoryofprobabilityProbabilitytheoryasabranchofmathematics,itstudiesthecontentgeneralincludetheprobabilityofrandomevents,theregularityofstatisticalindependenceanddeeperadministrativelevels.Probabilityisaquantitativeindexofthepossibilityofrandomevents.Inindependentrandomevents,ifaneventfrequencyinallevents,inalargerrangeofstablearoundafixedconstant.Youcanthinktheprobabilityoftheincidenttotheconstant.Foranyeventprobabilityvaluemustbebetween0and1.Thereisacertaintypeofrandomevents,ithastwocharacteristics:first,onlyafinitenumberofpossibleresults;Second,theresultsthepossibilityofthesame.Havethecharacteristicsofthetworandomphenomenoncalled"classicalsubscheme".Intheobjectiveworld,therearealargenumberofrandomphenomena,theresultofarandomphenomenonposesarandomevent.Ifthevariableisusedtodescribeeachrandomphenomenonasaresult,isknownasrandomvariables.Randomvariablehasafiniteandtheinfinite,andaccordingtothevariablevaluesisusuallydividedintodiscreterandomvariablesandthediscreterandomvariable.Listallpossiblevaluescanbeaccordingtocertainorder,sucharandomvariableiscalledadiscreterandomvariable;Ifpossiblevalueswithaninterval,unabletomaketheorderlist,therandomvariableiscalledadiscreterandomvariable.ThecontentofthemathematicalstatisticsIncludingsampling,optimumlineproblemofmathematicalstatistics,hypothesistesting,analysisofvariance,correlationanalysis,etc.Samplinginspectionistopairthroughsampleinvestigation,toinfertheoverallsituation.Exactlyhowmuchsampling,thisisaveryimportantproblem,therefore,isproducedinthesamplinginspection"smallsampletheory",thisisinthecaseofthesampleissmall,theanalysisjudgmenttheory.Alsocalledcurvefittingandoptimallineproblem.Someproblemsneedtobeaccordingtotheexperiencedatatofindatheoreticaldistributioncurve,sothatthewholeproblemgetunderstanding.Butaccordingtowhatprinciplesandtheoreticalcurve?Howtocompareoutofseveraldifferentcurveinthesameissue?Selectinggoodcurve,ishowtodeterminetheirerror?......Isbelongtothescopeoftheoptimumlineissuesofmathematicalstatistics.Hypothesistestingisonlyatthetimeofinspectionproductswithmathematicalstatisticalmethod,firstmakeahypothesis,accordingtotheresultofsamplinginreliabletoacertainextent,tojudgethenullhypothesis.Alsocalleddeviationanalysis,varianceanalysisistousetheconceptofvariancetoanalyzebyahandfulofexperimentcanmakethejudgment.Duetotherandomphenomenonisabundantinhumanpracticalactivities,probabilityandstatisticswiththedevelopmentofmodernindustryandagriculture,modernscienceandtechnologyandcontinuousdevelopment,whichformedmanyimportantbranch.Suchasstochasticprocess,informationtheory,experimentaldesign,limittheory,multivariateanalysis,etc.译文：概率论和数理统计简介概率论与数理统计是对随机现象的统计规律进行演绎和归纳的科学，从数量侧面研究随机现象的统计规律性的基础数学学科，概率论与数理统计又可分为概率论和数理统计两个分支。概率是用来刻画随机事件发生的可能性大小的量。概率论的主要内容包括古典概型的计算、随机变量的分布及特征数字和极限定理等等。数理统计乃数学中联系实际最直接最广泛的分支之一，它介绍了点估计(矩法估计、极大似然估计)、参数假设检验、非参数假设检验、方差分析和多元回归分析、、可靠性分析等基本知识和原理，使学生对统计学原理的作用有一深刻的了解。通过本课程的学习，使学生能全面理解、掌握概率论与数理统计的思想与方法，掌握基本而常用的分析和计算方法，并能运用概率论与数理统计的观点和方法来研究解决经济与管理中的实践问题。随机现象从随机现象说起，在自然界和现实生活中，一些事物都是相互联系和不断发展的。在它们彼此间的联系和发展中，根据它们是否有必然的因果联系，可以分成截然不同的两大类：一类是确定性的现象。这类现象是在一定条件下，必定会导致某种确定的结果。举例来说，在标准大气压下，水加热到100摄氏度，就必然会沸腾。事物间的这种联系是属于必然性的。通常的自然科学各学科就是专门研究和认识这种必然性的，寻求这类必然现象的因果关系，把握它们之间的数量规律。另一类是不确定性的现象。这类现象是在一定条件下，它的结果是不确定的。举例来说，同一个工人在同一台机床上加工同一种零件若干个，它们的尺寸总会有一点差异。又如，在同样条件下，进行小麦品种的人工催芽试验，各棵种子的发芽情况也不尽相同，有强弱和早晚的分别等等。为什么在相同的情况下，会出现这种不确定的结果呢？这是因为，我们说的“相同条件”是指一些主要条件来说的，除了这些主要条件外，还会有许多次要条件和偶然因素又是人们无法事先一一能够掌握的。正因为这样，我们在这一类现象中，就无法用必然性的因果关系，对个别现象的结果事先做出确定的答案。事物间的这种关系是属于偶然性的，这种现象叫做偶然现象，或者叫做随机现象。在自然界，在生产、生活中，随机现象十分普遍，也就是说随机现象是大量存在的。比如：每期体育彩票的中奖号码、同一条生产线上生产的灯泡的寿命等，都是随机现象。因此，我们说：随机现象就是：在同样条件下，多次进行同一试验或调查同一现象，所的结果不完全一样，而且无法准确地预测下一次所得结果的现象。随机现象这种结果的不确定性，是由于一些次要的、偶然的因素影响所造成的。随机现象从表面上看，似乎是杂乱无章的、没有什么规律的现象。但实践证明，如果同类的随机现象大量重复出现，它的总体就呈现出一定的规律性。大量同类随机现象所呈现的这种规律性，随着我们观察的次数的增多而愈加明显。比如掷硬币，每一次投掷很难判断是那一面朝上，但是如果多次重复的掷这枚硬币，就会越来越清楚的发现它们朝上的次数大体相同。我们把这种由大量同类随机现象所呈现出来的集体规律性，叫做统计规律性。概率论和数理统计就是研究大量同类随机现象的统计规律性的数学学科。概率论的产生和发展概率论产生于十七世纪，本来是由保险事业的发展而产生的，但是来自于赌博者的请求，却是数学家们思考概率论中问题的源泉。早在1654年，有一个赌徒梅累向当时的数学家帕斯卡提出一个使他苦恼了很久的问题：“两个赌徒相约赌若干局，谁先赢m局就算赢，全部赌本就归谁。但是当其中一个人赢了a(a<m)局，另一个人赢了b(b<m)局的时候，赌博中止。问：赌本应该如何分法才合理？”后者曾在1642年发明了世界上第一台机械加法计算机。三年后，也就是1657年，荷兰著名的天文、物理兼数学家惠更斯企图自己解决这一问题，结果写成了《论机会游戏的计算》一书，这就是最早的概率论著作。近几十年来，随着科技的蓬勃发展，概率论大量应用到国民经济、工农业生产及各学科领域。许多兴起的应用数学，如信息论、对策论、排队论、控制论等，都是以概率论作为基础的。概率论和数理统计是一门随机数学分支，它们是密切联系的同类学科。但是应该指出，概率论、数理统计、统计方法又都各有它们自己所包含的不同内容。概率论——是根据大量同类随机现象的统计规律，对随机现象出现某一结果的可能性作出一种客观的科学判断，对这种出现的可能性大小做出数量上的描述；比较这些可能性的大小、研究它们之间的联系，从而形成一整套数学理论和方法。数理统计——是应用概率的理论来研究大量随机现象的规律