Ch2 Probability Theory and Statistical Inference

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1、STAT4007StatisticalQualityControlChapter2ProbabilityTheoryandStatisticalInferenceDr.PhilipLee2012/13Term2Reference:Chapter3&4ofStatisticalQualityControl,DouglasC.Montgomery,6thEdition1BasicKnowledgeRequiringforStatisticalQualityControl•ProbabilityTheoryand

2、DistributionsinSTAT2001•StatisticalInferenceinSTAT2006•NewMaterialtobecoveredintheChapter:1.HypergeometricDistribution2.DeriveanUnbiasedEstimatorofStandardDeviationσ(notS!!).Notethat22E(S)butE(S)3.AbouttheRangeRandomVariableRXXmaxmin4.OperatingCharac

3、teristic(OC)CurveforTypeIIError2ChapterOutlineProbabilityTheory•Section2.1:ProbabilityDistribution•Section2.2:CommonProbabilityDistributionsforQualityControl•Section2.3:ApproximationofProbabilityDistributionsStatisticalInference•Section2.4:RandomSamplesand

4、SamplingDistribution•Section2.5:PointEstimations•Section2.6:TerminologiesinHypothesistesting•Section2.7:InferenceforSingleSample•Section2.8:InferenceforTwoSamples•Section2.9:DecisionErrorsandOperatingCharacteristicCurves3Section2.1ProbabilityDistribution4S

5、ampleSpace,Outcome,EventandProbabilityThesamplespaceisthesetofallpossibleoutcomes.Anoutcomeiseachpossibletypeofoccurrence.Aneventisanysetofoutcomesofinterest.Thesymbol{}isusedastheshorthandfor“theevent”.Theprobabilityofaneventistherelativefrequencyofas

6、etofoutcomesoveranindefinitelylargenumberoftrials.TheprobabilityofaneventE,denotedbyPr(E)[orP(E)],alwayssatisfies0≤Pr(E)≤1Ingeneral,NumberofoutcomesineventAPr(A)Numberofoutcomesinthesamplespace5SampleSpace,Outcome,EventandProbabilityExample:Supposeweflipa

7、faircoin3times.Whatistheprobabilityofobtainingoneheadand2tails?•SampleSpace={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}•PossibleOutcomes=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT•Eventofinterest={HTT,THT,TTH}•Probabilityofobtainingoneheadand2tails=3/86CumulativeDistributionFu

8、nction•CumulativeDistributionFunction(cdf)ofarandomvariableX,denotedbyF(x),isdefinedasXFX(x)P(Xx)forallxNotethatF(x)isanon-decreasingfunctionofxsuchthatXlimF(x)1andlimF(x)0XXxxExample:Fromtheprevious