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1、STAT145(Notes)AlNosedalanosedal@unm.eduDepartmentofMathematicsandStatisticsUniversityofNewMexicoFall2013......CHAPTER10INTRODUCINGPROBABILITY.......RandomnessandProbabilityWecallaphenomenonrandomifindividualoutcomesareuncertainbutthereisnonethelessaregulardistributionofoutcomesinalargenumber
2、ofrepetitions.Theprobabilityofanyoutcomeofarandomphenomenonistheproportionoftimestheoutcomewouldoccurinaverylongseriesofrepetitions.......Probabilitysays...Probabilityisameasureofhowlikelyaneventistooccur.Matchoneoftheprobabilitiesthatfollowwitheachstatementoflikelihoodgiven.(Theprobabilityi
3、susuallyamoreexactmeasureoflikelihoodthatistheverbalstatement.)00.010.450.500.550.991a)Theeventisimpossible.Itcanneveroccur.b)Thiseventiscertain.Itwilloccuroneverytrial.c)Theeventisverylikely,butonceinawhileitwillnotoccurinalongsequenceoftrials.d)Thiseventwilloccurslightlylessoftenthannot...
4、....Solutiona)Animpossibleeventhasprobability0.b)Acertaineventhasprobability1.c)0.99wouldcorrespondtoaneventthatisverylikelybutwillnotoccuronceinawhileinalongsequenceoftrials.d)Aneventwithprobability0.45willoccurslightlylessoftenthanitoccurs.......ProbabilityModelsThesamplespaceSofarandomphe
5、nomenonisthesetofallpossibleoutcomes.Aneventisanoutcomeorasetofoutcomesofarandomphenomenon.Thatis,aneventisasubsetofthesamplespace.Aprobabilitymodelisamathematicaldescriptionofarandomphenomenonconsistingoftwoparts:asamplespaceSandawayofassigningprobabilitiestoevents.......SamplespaceIneachof
6、thefollowingsituations,describeasamplespaceSfortherandomphenomenon.a.Abasketballplayershootsthreefreethrows.Yourecordthesequenceofhitsandmisses.b.Abasketballplayershootsthreefreethrows.Yourecordthenumberofbasketsshemakes.......SolutionH=hitandM=miss.a.S=f(H,H,H),(H,H,M),(H,M,H),(H,M,M),(M,H,
7、H),(M,H,M),(M,M,H),(M,M,M)gb.S=f0,1,2,3g......ColorsofM&MsIfyoudrawanM&Mcandyatrandomfromabagofthecandies,thecandyyoudrawwillhaveoneofthesevencolors.Theprobabilityofdrawingeachcolordependsontheproportionofeachcoloramongallcandiesmade.Hereisthedistr
