概率論與數(shù)理統(tǒng)計(jì)lec演示文稿

概率論與數(shù)理統(tǒng)計(jì)lec演示文稿目前一頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)概率論與數(shù)理統(tǒng)計(jì)lec目前二頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)TextbookandReferencesTextbook:JayL.Devore,Probabilityandstatisticsforengineeringandthesciences(6thed.),機(jī)械工業(yè)出版社,ISBN7-111-15724-9.References:茆詩(shī)松、程依明、濮曉龍，《概率論與數(shù)理統(tǒng)計(jì)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(jì)》（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(jì)》（第4版），北京：高等教育出版社，2008，ISBN7-040-23896-9目前三頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Whystudyprobabilityandstatistics?Theonlypurposefulimpactyouwillhaveonyourlifeandintheworldwillcomefromdecisionsyoumake.Whatmakesdecisionshard?Onethingthatmakesdecisionshardisuncertainty.目前四頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Whystudyprobabilityandstatistics?Weareabletoexplicitlyincludeuncertaintyintodecisionmakingusingprobability.Whathappensifyouignoreuncertaintyindecisionmaking?目前五頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Whatdowedowhenfacedwithuncertainty?Howdoyoudesignapolicyforclimatechange?Howdoyoudesignaculvertforfloodprevention?Planforthe“worstcase”?Planforthe“averagecase?”目前六頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)ExamplesPlanninganddesignofairportpavementThicker–lastslongerThicker–moreexpensiveRelationbetweenthicknessandlifeisuncertain.Therefore,thetotalcostoftheprojectisuncertain.目前七頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)ExamplesDesignofanoffshoredrillingtowerHowsafeissafeenough?Possibilityofhurricaneduringusefullife目前八頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Designofanoff-shorewindturbinefatiguelifeisunknownmustdesigntotradeoffinitialcostswithlifetimeandreliability目前九頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Whatisprobability?Uncertaintycanbeassessedordiscussedinformallyusinglanguagesuchas“itisunlikely”or“probably”.Probabilitymeasuresuncertaintyformally,quantitatively.It

isthemathematicallanguageofuncertainty."Itisremarkablethatasciencewhichbeganwiththeconsiderationofgamesofchanceshouldhavebecomethemostimportantobjectofhumanknowledge."——Pierre-SimonLaplace,ThéorieAnalytiquedesProbabilités,1812.目前十頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Whatisstatistics?Statisticsprovidedataaboutuncertainrelationships.Theyarenumbersthatsummarizetheresultsofastudy.Statisticalinferenceformalizestheprocessoflearningthroughobservation.Statisticsisthefieldthatstudieshowtoefficientlycollectinformativedata,exploreandinterpretthesedataanddrawconclusionsbasedonthem.目前十一頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Chapter1OverviewandDescriptiveStatistics1.1Populations,Samples,andProcess1.2PictorialandTabularMethodsinDescriptiveStatistics1.3MeasuresofLocation1.4MeasuresofVariability目前十二頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Introduction

Statisticalconceptsandmethodsarenotonlyusefulbutindeedoftenindispensableinunderstandingtheworldaroundus.Theyprovidewaysofgainingnewinsightsintothebehaviorofmanyphenomenathatyouwillencounterinyourchosenfieldofspecializationonengineeringorscience.Theprobability&statisticsisascienceofstudyingstatisticlawofrandomphenomena.Thisscienceisgeneratedfrom17thcentury,comesofgamblingandisappliedingambling.Butnowitisthefoundationofmanysciences,forexample,computerscience,informationscience,communicationengineering,controlscience,decisiontheory,gametheory,econometrics,etc.目前十三頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Thiscoursewillmainlyintroduceprobabilitybasicconceptsandstatisticsbasicmethodstostudents,includingtheConceptofProbability,RandomVariables,DistributionFunction,DensityFunction,Expectation,Variance,Independence,ConditionalProbability,SpecialDiscreteModels,SpecialContinuousModels,theConceptofStatistics,SamplingDistributions,ParameterEstimation,HypothesisTesting,andsoon.目前十四頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)1.1Populations,Samples,andProcessesEngineersandscientistsareconstantlyexposedtocollectionsoffacts,ordata,bothintheirprofessionalcapacitiesandineverydayactivities.Thedisciplineofstatisticsprovidesmethodsfororganizingandsummarizingdata,andfordrawingconclusionsbasedoninformationcontainedonthedata.Apopulation（總體）——

aninvestigationwilltypicallyfocusonawell-definedcollectionofobjects.Apopulationisthesetofallelementsofinterestinaparticularstudy.Forexample:(1)Allgelatincapsulesofaparticulartypeproducedduringaspecifiedperiod.(2)AllindividualswhoreceivedaB.S.inengineering.(3)Allstudentswho’smathematicsscoreabove70.目前十五頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Sample（樣本）Asample

isasubsetofthepopulation.Population=groupofpeople/objectsthatyoureallywanttoknowabout,e.g.,shipmentoflightbulbsSample=thegroupofpeople/objectsyouareactuallyabletoexamine,e.g.,5lightbulbsProbability:If10%ofthelightbulbsaredefectives,howmanywillIexpecttoseeinmysample?Statistics:IfIhave1badlightbulbinmysample,isthatstrongenoughevidencetoconvincemetonottaketheshipment?目前十六頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)PopulationSample目前十七頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)DataDataarethefactsandfiguresthatarecollected,analyzed,andsummarizedforpresentationandinterpretation.Together,thedatacollectedinaparticularstudyarereferredtoasthedatasetforthestudy.Table1.1showsadatasetcontainingfinancialinformationforsomecompanies,takenfromtheStockInvestorPpanyexchangeTickersymbolAnnualsalesSharepricePrice/earningsratioAwardsoftwraeOTCAWRD15.711.50022.5ChesapeakeenergyNYSECHK255.37.88012.7CraigcorporationNYSECRG29.417.0007.5EdistoAMEXEDT254.69.6886.0目前十八頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Elements,Variables,andObservations

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

Thesetofmeasurementscollectedforaparticularelementiscalledanobservation（觀察值）.目前十九頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)BranchesofStatisticsDescriptivestatistics（描述性統(tǒng)計(jì)）Aninvestigatorwhohascollecteddatamaywishsimplytosummarizeanddescribeimportantfeaturesofthedata.Thisentailsusingmethodsfromdescriptivestatistics.

Someofthesemethodsaregraphicalinnature;theconstructionofhistograms（直方圖）,boxplots（箱線(xiàn)圖）,andscatterplots（散點(diǎn)圖）areprimaryexamples.Otherdescriptivemethodsinvolvecalculationofnumericalsummarymeasures,suchasmeans,standard

deviations,andcorrelationscoefficients.目前二十頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Example1.1Hereisdataconsistingofobservationsonx=O-ringtemperatureforeachtestfiringoraactuallaunchoftheshuttlerocketengine2535455565758520103040目前二十一頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Inferentialstatistics（推斷統(tǒng)計(jì)）Amajorcontributionofstatisticsisthatdatafromasamplecanbeusedtomakeestimatesandtesthypothesesaboutthecharacteristicsofapopulation.Thisprocessisreferredtoasstatisticalinference（統(tǒng)計(jì)推斷）.Forexample:(1)10oflastyear’sengineeringgraduatestoobtainfeedbackaboutthequalityoftheengineeringcurricula.(2)Asampleofbearingsfromaparticularproductionrun.目前二十二頁(yè)\總數(shù)二十四頁(yè)\編于十五點(diǎn)Example1.2Materialstrengthinvestigationsprovidearichareaofapplicationforstatisticalmethods.Supposewehavethefollowingdataonflexuralstrength:7.07.011.611.311.810.7Nowwewantanestimateoftheaveragevalueofflexu