概率统计英文讲义Walpol

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1、Probability&StatisticsforEngineers&Scientists,byWalpole,Myers,Myers&Ye~Chapter2NotesClassnotesforISE201SanJoseStateUniversityIndustrial&SystemsEngineeringDept.SteveKennedyProbabilityIntroThesamplespaceSofanexperimentisthesetofallpossibleoutcomes.Wemustunderstandthesamplespaceinorderto

2、determinetheprobabilityofeachoutcomeoccurring.Thesamplespaceisaset,thedomainoftheprobabilityfunction.Eachprobabilityvalue,p,isarealnumber0p1.Important:Thesumoftheprobabilitiesforallelementsinthesamplespacealwaysequals1.Whyisthisimportant?Thisfactallowsustocheckouranswers.Properlyenumer

3、atingthesamplespaceiskeytocorrectlycalculatingprobabilities.Atreediagramissometimesuseful.EventsAneventisasubsetofasamplespace(ES)NotethatbothSandareeventsaswell.Samplespacescanbecontinuousordiscrete.Whatisacontinuousvs.discretesamplespace?Example:Lifeinyearsofacomponent.S=?S={t

4、t0}=>

5、“allvaluesoftsuchthatt0”A=componentfailsbeforetheendofthefifthyear.A={t

6、t<5}.Example:Flipacointhreetimes.S=?S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}EventA=1stflipisheads.A={HHH,HHT,HTH,HTT}Event/SetOperationsThecomplementofaneventA?ThesetofallelementsofSnotinA.DenotedA’.A=1stflipisheads.A’=f

7、irstflipisnotheads.TheintersectionoftwoeventsAandB?ThesetofallelementsinbothAandB.DenotedAB.B=2ndor3rdflip,butnotboth,areheads.B={HHT,HTH,THT,TTH}.AB=?AB={HHT,HTH}Twoeventsaremutuallyexclusiveif…?AB=Theunionoftwoevents,AandB?ThesetofelementsineitherAorB.AB=?AB={HHH,HHT,HTH,HTT,THT

8、,TTH}.VennDiagramsVennDiagramsshowvariouseventsgraphically,andaresometimeshelpfulinunderstandingsettheoryproblems.Standardsettheoryresultshold:A=?A=?AA’=?AA’=?S’=?’=?(A’)’=?(AB)’=?(AB)’=?(AB)’=A’B’,(AB)’=A’B’IntuitiveSamplePointCountingIfoneoperationcanbeperformedinn1ways,an

9、dforeachway,asecondcanbeperformedinn2ways,thenthetwocanbeperformedatotalofn1n2ways.Forthreeoperations?n1n2n3.Howmanypasswordsoflength5needtobecheckedbyapasswordhackingprogramifonlylowercaselettersareused?265=11,881,376.Thisiscalledsamplingwithreplacement.Atreediagramcanbe