概率論與數(shù)理統(tǒng)計(jì)英文文獻(xiàn)

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.譯文：概率論和數(shù)理統(tǒng)計(jì)簡介概率論與數(shù)理統(tǒng)計(jì)是對(duì)隨機(jī)現(xiàn)象的統(tǒng)計(jì)規(guī)律進(jìn)行演繹和歸納的科學(xué)，從數(shù)量側(cè)面研究隨機(jī)現(xiàn)象的統(tǒng)計(jì)規(guī)律性的基礎(chǔ)數(shù)學(xué)學(xué)科，概率論與數(shù)理統(tǒng)計(jì)又可分為概率論和數(shù)理統(tǒng)計(jì)兩個(gè)分支。概率是用來刻畫隨機(jī)事件發(fā)生的可能性大小的量。概率論的主要內(nèi)容包括古典概型的計(jì)算、隨機(jī)變量的分布及特征數(shù)字和極限定理等等。數(shù)理統(tǒng)計(jì)乃數(shù)學(xué)中聯(lián)系實(shí)際最直接最廣泛的分支之一，它介紹了點(diǎn)估計(jì)(矩法估計(jì)、極大似然估計(jì))、參數(shù)假設(shè)檢驗(yàn)、非參數(shù)假設(shè)檢驗(yàn)、方差分析和多元回歸分析、、可靠性分析等基本知識(shí)和原理，使學(xué)生對(duì)統(tǒng)計(jì)學(xué)原理的作用有一深刻的了解。通過本課程的學(xué)習(xí)，使學(xué)生能全面理解、掌握概率論與數(shù)理統(tǒng)計(jì)的思想與方法，掌握基本而常用的分析和計(jì)算方法，并能運(yùn)用概率論與數(shù)理統(tǒng)計(jì)的觀點(diǎn)和方法來研究解決經(jīng)濟(jì)與管理中的實(shí)踐問題。隨機(jī)現(xiàn)象從隨機(jī)現(xiàn)象說起，在自然界和現(xiàn)實(shí)生活中，一些事物都是相互聯(lián)系和不斷發(fā)展的。在它們彼此間的聯(lián)系和發(fā)展中，根據(jù)它們是否有必然的因果聯(lián)系，可以分成截然不同的兩大類：一類是確定性的現(xiàn)象。這類現(xiàn)象是在一定條件下，必定會(huì)導(dǎo)致某種確定的結(jié)果。舉例來說，在標(biāo)準(zhǔn)大氣壓下，水加熱到100攝氏度，就必然會(huì)沸騰。事物間的這種聯(lián)系是屬于必然性的。通常的自然科學(xué)各學(xué)科就是專門研究和認(rèn)識(shí)這種必然性的，尋求這類必然現(xiàn)象的因果關(guān)系，把握它們之間的數(shù)量規(guī)律。另一類是不確定性的現(xiàn)象。這類現(xiàn)象是在一定條件下，它的結(jié)果是不確定的。舉例來說，同一個(gè)工人在同一臺(tái)機(jī)床上加工同一種零件若干個(gè)，它們的尺寸總會(huì)有一點(diǎn)差異。又如，在同樣條件下，進(jìn)行小麥品種的人工催芽試驗(yàn)，各棵種子的發(fā)芽情況也不盡相同，有強(qiáng)弱和早晚的分別等等。為什么在相同的情況下，會(huì)出現(xiàn)這種不確定的結(jié)果呢？這是因?yàn)?，我們說的“相同條件”是指一些主要條件來說的，除了這些主要條件外，還會(huì)有許多次要條件和偶然因素又是人們無法事先一一能夠掌握的。正因?yàn)檫@樣，我們在這一類現(xiàn)象中，就無法用必然性的因果關(guān)系，對(duì)個(gè)別現(xiàn)象的結(jié)果事先做出確定的答案。事物間的這種關(guān)系是屬于偶然性的，這種現(xiàn)象叫做偶然現(xiàn)象，或者叫做隨機(jī)現(xiàn)象。在自然界，在生產(chǎn)、生活中，隨機(jī)現(xiàn)象十分普遍，也就是說隨機(jī)現(xiàn)象是大量存在的。比如：每期體育彩票的中獎(jiǎng)號(hào)碼、同一條生產(chǎn)線上生產(chǎn)的燈泡的壽命等，都是隨機(jī)現(xiàn)象。因此，我們說：隨機(jī)現(xiàn)象就是：在同樣條件下，多次進(jìn)行同一試驗(yàn)或調(diào)查同一現(xiàn)象，所的結(jié)果不完全一樣，而且無法準(zhǔn)確地預(yù)測下一次所得結(jié)果的現(xiàn)象。隨機(jī)現(xiàn)象這種結(jié)果的不確定性，是由于一些次要的、偶然的因素影響所造成的。隨機(jī)現(xiàn)象從表面上看，似乎是雜亂無章的、沒有什么規(guī)律的現(xiàn)象。但實(shí)踐證明，如果同類的隨機(jī)現(xiàn)象大量重復(fù)出現(xiàn)，它的總體就呈現(xiàn)出一定的規(guī)律性。大量同類隨機(jī)現(xiàn)象所呈現(xiàn)的這種規(guī)律性，隨著我們觀察的次數(shù)的增多而愈加明顯。比如擲硬幣，每一次投擲很難判斷是那一面朝上，但是如果多次重復(fù)的擲這枚硬幣，就會(huì)越來越清楚的發(fā)現(xiàn)它們朝上的次數(shù)大體相同。我們把這種由大量同類隨機(jī)現(xiàn)象所呈現(xiàn)出來的集體規(guī)律性，叫做統(tǒng)計(jì)規(guī)律性。概率論和數(shù)理統(tǒng)計(jì)就是研究大量同類隨機(jī)現(xiàn)象的統(tǒng)計(jì)規(guī)律性的數(shù)學(xué)學(xué)科。概率論的產(chǎn)生和發(fā)展概率論產(chǎn)生于十七世紀(jì)，本來是由保險(xiǎn)事業(yè)的發(fā)展而產(chǎn)生的，但是來自于賭博者的請求，卻是數(shù)學(xué)家們思考概率論中問題的源泉。早在1654年，有一個(gè)賭徒梅累向當(dāng)時(shí)的數(shù)學(xué)家帕斯卡提出一個(gè)使他苦惱了很久的問題：“兩個(gè)賭徒相約賭若干局，誰先贏m局就算贏，全部賭本就歸誰。但是當(dāng)其中一個(gè)人贏了a(a<m)局，另一個(gè)人贏了b(b<m)局的時(shí)候，賭博中止。問：賭本應(yīng)該如何分法才合理？”后者曾在1642年發(fā)明了世界上第一臺(tái)機(jī)械加法計(jì)算機(jī)。三年后，也就是1657年，荷蘭著名的天文、物理兼數(shù)學(xué)家惠更斯企圖自己解決這一問題，結(jié)果寫成了《論機(jī)會(huì)游戲的計(jì)算》一書，這就是最早的概率論著作。近幾十年來，隨著科技的蓬勃發(fā)展，概率論大量應(yīng)用到國民經(jīng)濟(jì)、工農(nóng)業(yè)生產(chǎn)及各學(xué)科領(lǐng)域。許多興起的應(yīng)用數(shù)學(xué)，如信息論、對(duì)策論、排隊(duì)論、控制論等，都是以概率論作為基礎(chǔ)的。概率論和數(shù)理統(tǒng)計(jì)是一門隨機(jī)數(shù)學(xué)分支，它們是密切聯(lián)系的同類學(xué)科。但是應(yīng)該指出，概率論、數(shù)理統(tǒng)計(jì)、統(tǒng)計(jì)方法又都各有它們自己所包含的不同內(nèi)容。概率論——是根據(jù)大量同類隨機(jī)現(xiàn)象的統(tǒng)計(jì)規(guī)律，對(duì)隨機(jī)現(xiàn)象出現(xiàn)某一結(jié)果的可能性作出一種客觀的科學(xué)判斷，對(duì)這種出現(xiàn)的可能性大小做出數(shù)量上的描述；比較這些可能性的大小、研究它們之間的聯(lián)系，從而形成一整套數(shù)學(xué)理論和方法。數(shù)理統(tǒng)計(jì)——是應(yīng)用概率的理論來研究大量隨機(jī)現(xiàn)象的規(guī)律