统计学第五章

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1、ASurveyofProbabilityConceptsChapter5GOALSDefineprobability.Describetheclassical,empirical,andsubjectiveapproachestoprobability.Explainthetermsexperiment,event,outcome,permutations,andcombinations.Definethetermsconditionalprobabilityandjointprobability.Calculateprobabilitiesusing

2、therulesofadditionandrulesofmultiplication.Applyatreediagramtoorganizeandcomputeprobabilities.CalculateaprobabilityusingBayes’theorem.2DefinitionsAprobabilityisameasureofthelikelihoodthataneventinthefuturewillhappen.Ititcanonlyassumeavaluebetween0and1.Avaluenearzeromeanstheevent

3、isnotlikelytohappen.Avaluenearonemeansitislikely.Therearethreewaysofassigningprobability:classical,empirical,andsubjective.3ProbabilityExamples4DefinitionscontinuedAnexperimentistheobservationofsomeactivityortheactoftakingsomemeasurement.Anoutcomeistheparticularresultofanexperim

4、ent.Aneventisthecollectionofoneormoreoutcomesofanexperiment.5Experiments,EventsandOutcomes6AssigningProbabilitiesThreeapproachestoassigningprobabilitiesClassicalEmpiricalSubjective7ClassicalProbabilityConsideranexperimentofrollingasix-sideddie.Whatistheprobabilityoftheevent“anev

5、ennumberofspotsappearfaceup”?Thepossibleoutcomesare:Therearethree“favorable”outcomes(atwo,afour,andasix)inthecollectionofsixequallylikelypossibleoutcomes.8MutuallyExclusiveEventsEventsaremutuallyexclusiveiftheoccurrenceofanyoneeventmeansthatnoneoftheotherscanoccuratthesametime.E

6、ventsareindependentiftheoccurrenceofoneeventdoesnotaffecttheoccurrenceofanother.9CollectivelyExhaustiveEventsEventsarecollectivelyexhaustiveifatleastoneoftheeventsmustoccurwhenanexperimentisconducted.10EmpiricalProbabilityTheempiricalapproachtoprobabilityisbasedonwhatiscalledthe

7、lawoflargenumbers.Thekeytoestablishingprobabilitiesempiricallyisthatmoreobservationswillprovideamoreaccurateestimateoftheprobability.11LawofLargeNumbersSupposewetossafaircoin.Theresultofeachtossiseitheraheadoratail.Ifwetossthecoinagreatnumberoftimes,theprobabilityoftheoutcomeofh

8、eadswillapproach.5.Thefollowingtablereportsther