概率论与数理统计lec

概率论与数理统计lec01TextbookandReferencesTextbook:JayL.Devore,Probabilityandstatisticsforengineeringandthesciences(6thed.),机械工业出版社,ISBN7-111-15724-9.References:茆诗松、程依明、濮晓龙，《概率论与数理统计教程》，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

影印改编版：章栋恩改编，《概率论与数理统计》（第7版），北京：电子工业出版社，2005，ISBN7-121-01931-0盛骤、谢式千、潘承毅，《概率论与数理统计》（第4版），北京：高等教育出版社，2008，ISBN7-040-23896-92Whystudyprobabilityandstatistics?Theonlypurposefulimpactyouwillhaveonyourlifeandintheworldwillcomefromdecisionsyoumake.Whatmakesdecisionshard?Onethingthatmakesdecisionshardisuncertainty.3Whystudyprobabilityandstatistics?Weareabletoexplicitlyincludeuncertaintyintodecisionmakingusingprobability.Whathappensifyouignoreuncertaintyindecisionmaking?4Whatdowedowhenfacedwithuncertainty?Howdoyoudesignapolicyforclimatechange?Howdoyoudesignaculvertforfloodprevention?Planforthe“worstcase”?Planforthe“averagecase?”5ExamplesPlanninganddesignofairportpavementThicker–lastslongerThicker–moreexpensiveRelationbetweenthicknessandlifeisuncertain.Therefore,thetotalcostoftheprojectisuncertain.6ExamplesDesignofanoffshoredrillingtowerHowsafeissafeenough?Possibilityofhurricaneduringusefullife7大家学习辛苦了，还是要坚持继续保持安静8Designofanoff-shorewindturbinefatiguelifeisunknownmustdesigntotradeoffinitialcostswithlifetimeandreliability9Whatisprobability?Uncertaintycanbeassessedordiscussedinformallyusinglanguagesuchas“itisunlikely”or“probably”.Probabilitymeasuresuncertaintyformally,quantitatively.It

isthemathematicallanguageofuncertainty."Itisremarkablethatasciencewhichbeganwiththeconsiderationofgamesofchanceshouldhavebecomethemostimportantobjectofhumanknowledge."——Pierre-SimonLaplace,ThéorieAnalytiquedesProbabilités,1812.10Whatisstatistics?Statisticsprovidedataaboutuncertainrelationships.Theyarenumbersthatsummarizetheresultsofastudy.Statisticalinferenceformalizestheprocessoflearningthroughobservation.Statisticsisthefieldthatstudieshowtoefficientlycollectinformativedata,exploreandinterpretthesedataanddrawconclusionsbasedonthem.11Chapter1OverviewandDescriptiveStatistics12Introduction

Statisticalconceptsandmethodsarenotonlyusefulbutindeedoftenindispensableinunderstandingtheworldaroundus.Theyprovidewaysofgainingnewinsightsintothebehaviorofmanyphenomenathatyouwillencounterinyourchosenfieldofspecializationonengineeringorscience.Theprobability&statisticsisascienceofstudyingstatisticlawofrandomphenomena.Thisscienceisgeneratedfrom17thcentury,comesofgamblingandisappliedingambling.Butnowitisthefoundationofmanysciences,forexample,computerscience,informationscience,communicationengineering,controlscience,decisiontheory,gametheory,econometrics,etc.1314Engineersandscientistsareconstantlyexposedtocollectionsoffacts,ordata,bothintheirprofessionalcapacitiesandineverydayactivities.Thedisciplineofstatisticsprovidesmethodsfororganizingandsummarizingdata,andfordrawingconclusionsbasedoninformationcontainedonthedata.Apopulation（总体）——

aninvestigationwilltypicallyfocusonawell-definedcollectionofobjects.Apopulationisthesetofallelementsofinterestinaparticularstudy.Forexample:(1)Allgelatincapsulesofaparticulartypeproducedduringaspecifiedperiod.(2)AllindividualswhoreceivedaB.S.inengineering.(3)Allstudentswho’smathematicsscoreabove70.1516Population17DataDataarethefactsandfiguresthatarecollected,analyzed,andsummarizedforpresentationandinterpretation.Together,thedatacollectedinaparticularstudyarereferredtoasthedatasetforthestudy.Table1.1showsadatasetcontainingfinancialinformationforsomecompanies,takenfromtheStockInvestorProdatabase.18Elements,Variables,andObservations

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

Thesetofmeasurementscollectedforaparticularelementiscalledanobservation（观察值）.19BranchesofStatisticsDescriptivestatistics（描述性统计）Aninvestigatorwhohascollecteddatamaywishsimplytosummarizeanddescribeimportantfeaturesofthedata.Thisentailsusingmethodsfromdescriptivestatistics.Someofthesemethodsaregraphicalinnature;theconstructionofhistograms（直方图）,boxplots（箱线图）,andscatterplots（散点图）areprimaryexamples.Otherdescriptivemethodsinvolvecalculationofnumericalsummarymeasures,suchasmeans,standarddeviations,andcorrelationscoefficients.2025354555657585201030402122Example1.2Materialstrengthinvestigationsprovidearicha