英文商务统计学ppt-第五章Ch05

BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-1Chapter5SomeImportantDiscreteProbabilityDistributionsBusinessStatistics:AFirstCourse

5thEditionBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-2LearningObjectivesInthischapter,youlearn:

ThepropertiesofaprobabilitydistributionTocalculatetheexpectedvalueandvarianceofaprobabilitydistributionTocalculateprobabilitiesfrombinomialandPoissondistributionsHowtousethebinomialandPoissondistributionstosolvebusinessproblemsBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-3Definitions

RandomVariablesArandomvariablerepresentsapossiblenumericalvaluefromanuncertainevent.Discreterandomvariablesproduceoutcomesthatcomefromacountingprocess(e.g.numberofcoursesyouaretakingthissemester).Continuousrandomvariablesproduceoutcomesthatcomefromameasurement(e.g.yourannualsalary,oryourweight).BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-4Definitions

RandomVariablesRandomVariablesDiscreteRandomVariableContinuousRandomVariableCh.5Ch.6Definitions

RandomVariablesRandomVariablesDiscreteRandomVariableContinuousRandomVariableCh.5Ch.6Definitions

RandomVariablesRandomVariablesDiscreteRandomVariableContinuousRandomVariableCh.5Ch.6BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-5DiscreteRandomVariablesCanonlyassumeacountablenumberofvaluesExamples:Rolladietwice LetXbethenumberoftimes4occurs (thenXcouldbe0,1,or2times)Tossacoin5times. LetXbethenumberofheads(thenX=0,1,2,3,4,or5)BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-6ProbabilityDistributionForADiscreteRandomVariableAprobabilitydistributionforadiscreterandomvariableisamutuallyexclusivelistingofallpossiblenumericaloutcomesforthatvariableandaprobabilityofoccurrenceassociatedwitheachoutcome.NumberofClassesTakenProbability20.230.440.2450.16BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-7Experiment:Toss2Coins.LetX=#heads.TTExampleofaDiscreteRandomVariableProbabilityDistribution4possibleoutcomesTTHHHHProbabilityDistribution012XXValue

Probability01/4=0.2512/4=0.5021/4=0.250.500.25

Probability

BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-8DiscreteRandomVariables

ExpectedValue(MeasuringCenter)

ExpectedValue(ormean)ofadiscreterandomvariable(WeightedAverage)

Example:Toss2coins, X=#ofheads, computeexpectedvalueofX:

E(X)=((0)(0.25)+(1)(0.50)+(2)(0.25))=1.0XP(X)00.2510.5020.25BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-9VarianceofadiscreterandomvariableStandardDeviationofadiscreterandomvariable where:

E(X)=ExpectedvalueofthediscreterandomvariableX Xi=theithoutcomeofX P(Xi)=ProbabilityoftheithoccurrenceofXDiscreteRandomVariables

MeasuringDispersionBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-10Example:Toss2coins,X=#heads, computestandarddeviation(recallE(X)=1)DiscreteRandomVariables

MeasuringDispersion(continued)Possiblenumberofheads=0,1,or2BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-11ProbabilityDistributionsContinuous

ProbabilityDistributionsBinomialPoissonProbabilityDistributionsDiscrete

ProbabilityDistributionsNormalCh.5Ch.6BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-12BinomialProbabilityDistributionAfixednumberofobservations,ne.g.,15tossesofacoin;tenlightbulbstakenfromawarehouseEachobservationiscategorizedastowhetherornotthe“eventofinterest”occurrede.g.,headortailineachtossofacoin;defectiveornotdefectivelightbulbSincethesetwocategoriesaremutuallyexclusiveandcollectivelyexhaustiveWhentheprobabilityoftheeventofinterestisrepresentedasπ,thentheprobabilityoftheeventofinterestnotoccurringis1-πConstantprobabilityfortheeventofinterestoccurring(π)foreachobservationProbabilityofgettingatailisthesameeachtimewetossthecoinBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-13BinomialProbabilityDistribution(continued)ObservationsareindependentTheoutcomeofoneobservationdoesnotaffecttheoutcomeoftheotherTwosamplingmethodsdeliverindependenceInfinitepopulationwithoutreplacementFinitepopulationwithreplacementBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-14PossibleApplicationsfortheBinomialDistributionAmanufacturingplantlabelsitemsaseitherdefectiveoracceptableAfirmbiddingforcontractswilleithergetacontractornotAmarketingresearchfirmreceivessurveyresponsesof“yesIwillbuy”or“noIwillnot”NewjobapplicantseitheraccepttheofferorrejectitBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-15TheBinomialDistribution

CountingTechniquesSupposetheeventofinterestisobtainingheadsonthetossofafaircoin.Youaretotossthecointhreetimes.Inhowmanywayscanyougettwoheads?Possibleways:HHT,HTH,THH,sotherearethreewaysyoucangettingtwoheads.Thissituationisfairlysimple.Weneedtobeabletocountthenumberofwaysformorecomplicatedsituations.BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-16CountingTechniques

RuleofCombinationsThenumberofcombinationsofselectingXobjectsoutofnobjectsiswhere: n!=(n)(n-1)(n-2)...(2)(1) X!=(X)(X-1)(X-2)...(2)(1) 0!=1(bydefinition)BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-17CountingTechniques

RuleofCombinationsHowmanypossible3scoopcombinationscouldyoucreateatanicecreamparlorifyouhave31flavorstoselectfrom?Thetotalchoicesisn=31,andweselectX=3.BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-18P(X)=probabilityofXeventsofinterestinntrials,withtheprobabilityofan“eventofinterest”beingπ

foreachtrialX=numberof“eventsofinterest”insample,(X=0,1,2,...,n)n=samplesize(numberoftrials orobservations)

π=probabilityof“eventofinterest”P(X)nX!nXπ(1-π)XnX!()!=--Example:Flipacoinfourtimes,letx=#heads:n=4π=0.51-π=(1-0.5)=0.5X=0,1,2,3,4BinomialDistributionFormulaBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-19Example:

CalculatingaBinomialProbabilityWhatistheprobabilityofonesuccessinfiveobservationsiftheprobabilityofaneventofinterestis.1? X=1,n=5,andπ=0.1BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-20TheBinomialDistribution

ExampleSupposetheprobabilityofpurchasingadefectivecomputeris0.02.Whatistheprobabilityofpurchasing2defectivecomputersinagroupof10? X=2,n=10,andπ=.02BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-21TheBinomialDistribution

Shapen=5π=0.10.2.4.6012345XP(X)n=5π=0.5.2.4.6012345XP(X)0TheshapeofthebinomialdistributiondependsonthevaluesofπandnHere,n=5andπ=.1Here,n=5andπ=.5BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-22TheBinomialDistribution

UsingBinomialTablesn=10x…π=.20π=.25π=.30π=.35π=.40π=.45π=.50012345678910……………………………0.10740.26840.30200.20130.08810.02640.00550.00080.00010.00000.00000.05630.18770.28160.25030.14600.05840.01620.00310.00040.00000.00000.02820.12110.23350.26680.20010.10290.03680.00900.00140.00010.00000.01350.07250.17570.25220.23770.15360.06890.02120.00430.00050.00000.00600.04030.12090.21500.25080.20070.11150.04250.01060.00160.00010.00250.02070.07630.16650.23840.23400.15960.07460.02290.00420.00030.00100.00980.04390.11720.20510.24610.20510.11720.04390.00980.0010109876543210…π=.80π=.75π=.70π=.65π=.60π=.55π=.50xExamples:n=10,π=.35,x=3:P(x=3|n=10,π=.35)=.2522n=10,π=.75,x=2:P(x=2|n=10,π=.75)=.0004BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-23BinomialDistributionCharacteristicsMeanVarianceandStandardDeviationWhere n=samplesize

π=probabilityoftheeventofinterestforanytrial (1–π)=probabilityofnoeventofinterestforanytrialBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-24TheBinomialDistribution

Characteristicsn=5π=0.10.2.4.6012345XP(X)n=5π=0.5.2.4.6012345XP(X)0ExamplesBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-25UsingExcelForThe

BinomialDistributionBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-26ThePoissonDistribution

DefinitionsYouusethePoissondistributionwhenyouareinterestedinthenumberoftimesaneventoccursinagivenareaofopportunity.Anareaofopportunityisacontinuousunitorintervaloftime,volume,orsuchareainwhichmorethanoneoccurrenceofaneventcanoccur.Thenumberofscratchesinacar’spaintThenumberofmosquitobitesonapersonThenumberofcomputercrashesinadayBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-27ThePoissonDistributionApplythePoissonDistributionwhen:YouwishtocountthenumberoftimesaneventoccursinagivenareaofopportunityTheprobabilitythataneventoccursinoneareaofopportunityisthesameforallareasofopportunity

ThenumberofeventsthatoccurinoneareaofopportunityisindependentofthenumberofeventsthatoccurintheotherareasofopportunityTheprobabilitythattwoormoreeventsoccurinanareaofopportunityapproacheszeroastheareaofopportunitybecomessmallerTheaveragenumberofeventsperunitis

(lambda)BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-28PoissonDistributionFormulawhere: X=numberofeventsinanareaofopportunity

=expectednumberofevents e=baseofthenaturallogarithmsystem(2.71828...)

BusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-29PoissonDistributionCharacteristicsMeanVarianceandStandardDeviationwhere

=expectednumberofeventsBusinessStatistics:AFirstCourse,5e©2009Prentice-Hall,Inc.Chap5-30UsingPoissonTablesX

0.100.200.300.400.500.600.700.800.90012345670.90480.09050.00450.00020.00000.00000.000