概率論與數(shù)理統(tǒng)計lec演示文稿

概率論與數(shù)理統(tǒng)計lec演示文稿當前第1頁\共有24頁\編于星期五\2點概率論與數(shù)理統(tǒng)計lec當前第2頁\共有24頁\編于星期五\2點TextbookandReferencesTextbook:JayL.Devore,Probabilityandstatisticsforengineeringandthesciences(6thed.),機械工業(yè)出版社,ISBN7-111-15724-9.References:茆詩松、程依明、濮曉龍，《概率論與數(shù)理統(tǒng)計教程》，北京：高等教育出版社，2004，ISBN7-040-14365-2R.Johnson,Miller&Freund’sProbabilityandStatisticsforEngineers,7thEd.PearsonEducation,2005,ISBN0-131-43745-6

影印改編版：章棟恩改編，《概率論與數(shù)理統(tǒng)計》（第7版），北京：電子工業(yè)出版社，2005，ISBN7-121-01931-0盛驟、謝式千、潘承毅，《概率論與數(shù)理統(tǒng)計》（第4版），北京：高等教育出版社，2008，ISBN7-040-23896-9當前第3頁\共有24頁\編于星期五\2點Whystudyprobabilityandstatistics?Theonlypurposefulimpactyouwillhaveonyourlifeandintheworldwillcomefromdecisionsyoumake.Whatmakesdecisionshard?Onethingthatmakesdecisionshardisuncertainty.當前第4頁\共有24頁\編于星期五\2點Whystudyprobabilityandstatistics?Weareabletoexplicitlyincludeuncertaintyintodecisionmakingusingprobability.Whathappensifyouignoreuncertaintyindecisionmaking?當前第5頁\共有24頁\編于星期五\2點Whatdowedowhenfacedwithuncertainty?Howdoyoudesignapolicyforclimatechange?Howdoyoudesignaculvertforfloodprevention?Planforthe“worstcase”?Planforthe“averagecase?”當前第6頁\共有24頁\編于星期五\2點ExamplesPlanninganddesignofairportpavementThicker–lastslongerThicker–moreexpensiveRelationbetweenthicknessandlifeisuncertain.Therefore,thetotalcostoftheprojectisuncertain.當前第7頁\共有24頁\編于星期五\2點ExamplesDesignofanoffshoredrillingtowerHowsafeissafeenough?Possibilityofhurricaneduringusefullife當前第8頁\共有24頁\編于星期五\2點Designofanoff-shorewindturbinefatiguelifeisunknownmustdesigntotradeoffinitialcostswithlifetimeandreliability當前第9頁\共有24頁\編于星期五\2點Whatisprobability?Uncertaintycanbeassessedordiscussedinformallyusinglanguagesuchas“itisunlikely”or“probably”.Probabilitymeasuresuncertaintyformally,quantitatively.It

isthemathematicallanguageofuncertainty."Itisremarkablethatasciencewhichbeganwiththeconsiderationofgamesofchanceshouldhavebecomethemostimportantobjectofhumanknowledge."——Pierre-SimonLaplace,ThéorieAnalytiquedesProbabilités,1812.當前第10頁\共有24頁\編于星期五\2點Whatisstatistics?Statisticsprovidedataaboutuncertainrelationships.Theyarenumbersthatsummarizetheresultsofastudy.Statisticalinferenceformalizestheprocessoflearningthroughobservation.Statisticsisthefieldthatstudieshowtoefficientlycollectinformativedata,exploreandinterpretthesedataanddrawconclusionsbasedonthem.當前第11頁\共有24頁\編于星期五\2點Chapter1OverviewandDescriptiveStatistics1.1Populations,Samples,andProcess1.2PictorialandTabularMethodsinDescriptiveStatistics1.3MeasuresofLocation1.4MeasuresofVariability當前第12頁\共有24頁\編于星期五\2點Introduction

Statisticalconceptsandmethodsarenotonlyusefulbutindeedoftenindispensableinunderstandingtheworldaroundus.Theyprovidewaysofgainingnewinsightsintothebehaviorofmanyphenomenathatyouwillencounterinyourchosenfieldofspecializationonengineeringorscience.Theprobability&statisticsisascienceofstudyingstatisticlawofrandomphenomena.Thisscienceisgeneratedfrom17thcentury,comesofgamblingandisappliedingambling.Butnowitisthefoundationofmanysciences,forexample,computerscience,informationscience,communicationengineering,controlscience,decisiontheory,gametheory,econometrics,etc.當前第13頁\共有24頁\編于星期五\2點Thiscoursewillmainlyintroduceprobabilitybasicconceptsandstatisticsbasicmethodstostudents,includingtheConceptofProbability,RandomVariables,DistributionFunction,DensityFunction,Expectation,Variance,Independence,ConditionalProbability,SpecialDiscreteModels,SpecialContinuousModels,theConceptofStatistics,SamplingDistributions,ParameterEstimation,HypothesisTesting,andsoon.當前第14頁\共有24頁\編于星期五\2點1.1Populations,Samples,andProcessesEngineersandscientistsareconstantlyexposedtocollectionsoffacts,ordata,bothintheirprofessionalcapacitiesandineverydayactivities.Thedisciplineofstatisticsprovidesmethodsfororganizingandsummarizingdata,andfordrawingconclusionsbasedoninformationcontainedonthedata.Apopulation（總體）——

aninvestigationwilltypicallyfocusonawell-definedcollectionofobjects.Apopulationisthesetofallelementsofinterestinaparticularstudy.Forexample:(1)Allgelatincapsulesofaparticulartypeproducedduringaspecifiedperiod.(2)AllindividualswhoreceivedaB.S.inengineering.(3)Allstudentswho’smathematicsscoreabove70.當前第15頁\共有24頁\編于星期五\2點Sample（樣本）Asample

isasubsetofthepopulation.Population=groupofpeople/objectsthatyoureallywanttoknowabout,e.g.,shipmentoflightbulbsSample=thegroupofpeople/objectsyouareactuallyabletoexamine,e.g.,5lightbulbsProbability:If10%ofthelightbulbsaredefectives,howmanywillIexpecttoseeinmysample?Statistics:IfIhave1badlightbulbinmysample,isthatstrongenoughevidencetoconvincemetonottaketheshipment?當前第16頁\共有24頁\編于星期五\2點PopulationSample當前第17頁\共有24頁\編于星期五\2點DataDataarethefactsandfiguresthatarecollected,analyzed,andsummarizedforpresentationandinterpretation.Together,thedatacollectedinaparticularstudyarereferredtoasthedatasetforthestudy.Table1.1showsadatasetcontainingfinancialinformationforsomecompanies,takenfromtheStockInvestorProdatabase.companyexchangeTickersymbolAnnualsalesSharepricePrice/earningsratioAwardsoftwraeOTCAWRD15.711.50022.5ChesapeakeenergyNYSECHK255.37.88012.7CraigcorporationNYSECRG29.417.0007.5EdistoAMEXEDT254.69.6886.0當前第18頁\共有24頁\編于星期五\2點Elements,Variables,andObservations

Theelementsaretheentitiesonwhichdataarecollected.Forthedataintable1.1,eachcompanyisanelement.Avariableisacharacteristicofinterestfortheelements.x=genderofagraduatingengineery=numberofmajordefectsonanewlymanufacturedautomobilez=brakingdistanceofanautomobileunderspecifiedconditionsAunivariate（單變）datasetconsistsofobservationsonasinglevariableBivariate（雙變）datameansobservationsaremadeoneachoftwovariables.

Thesetofmeasurementscollectedforaparticularelementiscalledanobservation（觀察值）.當前第19頁\共有24頁\編于星期五\2點BranchesofStatisticsDescriptivestatistics（描述性統(tǒng)計）Aninvestigatorwhohascollecteddatamaywishsimplytosummarizeanddescribeimportantfeaturesofthedata.Thisentailsusingmethodsfromdescriptivestatistics.

Someofthesemethodsaregraphicalinnature;theconstructionofhistograms（直方圖）,boxplots（箱線圖）,andscatterplots（散點圖）areprimaryexamples.Otherdescriptivemethodsinvolvecalculationofnumericalsummarymeasures,suchasmeans,standard

deviations,andcorrelationscoefficients.當前第20頁\共有24頁\編于星期五\2點Example1.1Hereisdataconsistingofobservationsonx=O-ringtemperatureforeachtestfiringoraactuallaunchoftheshuttlerocketengine2535455565758520103040當前第21頁\共有24頁\編于星期五\2點Inferentialstatistics（推斷統(tǒng)計）Amajorcontributionofstatisticsisthatdatafromasamplecanbeusedtomakeestimatesandtesthypothesesaboutthecharacteristicsofapopulation.Thisprocessisreferredtoasstatisticalinference（統(tǒng)計推斷）.Forexample:(1)10oflastyear’sengineeringgraduatestoobtainfeedbackaboutthequalityoftheengineeringcurricula.(2)Asampleofbearingsfromaparticularproductionrun.當前第22頁\共有24頁\編于星期五\2點Example1.2Materialstrengthinvestigationsprovidearichareaofapplicationforstatisticalmethods.Supposewehavethefollowingdataonflexuralstrength:5.97.27.36.38.16.87.07.66.86.57.06.37.99.08.28.77.89.77.47.79.77.87.711.611.311.810.7Nowwewantanestimateoftheaveragevalueoffl