商务统计学(英)5th.ppt

BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 1 Chapter5SomeImportantDiscreteProbabilityDistributions BusinessStatistics AFirstCourse5thEdition BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 2 LearningObjectives Inthischapter youlearn ThepropertiesofaprobabilitydistributionTocalculatetheexpectedvalueandvarianceofaprobabilitydistributionTocalculateprobabilitiesfrombinomialandPoissondistributionsHowtousethebinomialandPoissondistributionstosolvebusinessproblems BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 3 DefinitionsRandomVariables Arandomvariablerepresentsapossiblenumericalvaluefromanuncertainevent Discreterandomvariablesproduceoutcomesthatcomefromacountingprocess e g numberofcoursesyouaretakingthissemester Continuousrandomvariablesproduceoutcomesthatcomefromameasurement e g yourannualsalary oryourweight BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 4 DefinitionsRandomVariables RandomVariables DiscreteRandomVariable ContinuousRandomVariable Ch 5 Ch 6 DefinitionsRandomVariables RandomVariables DiscreteRandomVariable ContinuousRandomVariable Ch 5 Ch 6 DefinitionsRandomVariables RandomVariables DiscreteRandomVariable ContinuousRandomVariable Ch 5 Ch 6 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 5 DiscreteRandomVariables CanonlyassumeacountablenumberofvaluesExamples RolladietwiceLetXbethenumberoftimes4occurs thenXcouldbe0 1 or2times Tossacoin5times LetXbethenumberofheads thenX 0 1 2 3 4 or5 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 6 ProbabilityDistributionForADiscreteRandomVariable Aprobabilitydistributionforadiscreterandomvariableisamutuallyexclusivelistingofallpossiblenumericaloutcomesforthatvariableandaprobabilityofoccurrenceassociatedwitheachoutcome BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 7 Experiment Toss2Coins LetX heads T T ExampleofaDiscreteRandomVariableProbabilityDistribution 4possibleoutcomes T T H H H H ProbabilityDistribution 012X XValueProbability01 4 0 2512 4 0 5021 4 0 25 0 500 25 Probability BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 8 DiscreteRandomVariablesExpectedValue MeasuringCenter ExpectedValue ormean ofadiscreterandomvariable WeightedAverage Example Toss2coins X ofheads computeexpectedvalueofX E X 0 0 25 1 0 50 2 0 25 1 0 XP X 00 2510 5020 25 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 9 VarianceofadiscreterandomvariableStandardDeviationofadiscreterandomvariablewhere E X ExpectedvalueofthediscreterandomvariableXXi theithoutcomeofXP Xi ProbabilityoftheithoccurrenceofX DiscreteRandomVariablesMeasuringDispersion BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 10 Example Toss2coins X heads computestandarddeviation recallE X 1 DiscreteRandomVariablesMeasuringDispersion continued Possiblenumberofheads 0 1 or2 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 11 ProbabilityDistributions ContinuousProbabilityDistributions Binomial Poisson ProbabilityDistributions DiscreteProbabilityDistributions Normal Ch 5 Ch 6 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 12 BinomialProbabilityDistribution Afixednumberofobservations ne g 15tossesofacoin tenlightbulbstakenfromawarehouseEachobservationiscategorizedastowhetherornotthe eventofinterest occurrede g headortailineachtossofacoin defectiveornotdefectivelightbulbSincethesetwocategoriesaremutuallyexclusiveandcollectivelyexhaustiveWhentheprobabilityoftheeventofinterestisrepresentedas thentheprobabilityoftheeventofinterestnotoccurringis1 Constantprobabilityfortheeventofinterestoccurring foreachobservationProbabilityofgettingatailisthesameeachtimewetossthecoin BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 13 BinomialProbabilityDistribution continued ObservationsareindependentTheoutcomeofoneobservationdoesnotaffecttheoutcomeoftheotherTwosamplingmethodsdeliverindependenceInfinitepopulationwithoutreplacementFinitepopulationwithreplacement BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 14 PossibleApplicationsfortheBinomialDistribution AmanufacturingplantlabelsitemsaseitherdefectiveoracceptableAfirmbiddingforcontractswilleithergetacontractornotAmarketingresearchfirmreceivessurveyresponsesof yesIwillbuy or noIwillnot Newjobapplicantseitheraccepttheofferorrejectit BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 15 TheBinomialDistributionCountingTechniques Supposetheeventofinterestisobtainingheadsonthetossofafaircoin Youaretotossthecointhreetimes Inhowmanywayscanyougettwoheads Possibleways HHT HTH THH sotherearethreewaysyoucangettingtwoheads Thissituationisfairlysimple Weneedtobeabletocountthenumberofwaysformorecomplicatedsituations BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 16 CountingTechniquesRuleofCombinations ThenumberofcombinationsofselectingXobjectsoutofnobjectsis where 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 17 CountingTechniquesRuleofCombinations Howmanypossible3scoopcombinationscouldyoucreateatanicecreamparlorifyouhave31flavorstoselectfrom Thetotalchoicesisn 31 andweselectX 3 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 18 P X probabilityofXeventsofinterestinntrials withtheprobabilityofan eventofinterest being foreachtrialX numberof eventsofinterest insample X 0 1 2 n n samplesize numberoftrialsorobservations probabilityof eventofinterest P X n X n X 1 X n X Example Flipacoinfourtimes letx heads n 4 0 51 1 0 5 0 5X 0 1 2 3 4 BinomialDistributionFormula BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 19 Example CalculatingaBinomialProbability Whatistheprobabilityofonesuccessinfiveobservationsiftheprobabilityofaneventofinterestis 1 X 1 n 5 and 0 1 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 20 TheBinomialDistributionExample Supposetheprobabilityofpurchasingadefectivecomputeris0 02 Whatistheprobabilityofpurchasing2defectivecomputersinagroupof10 X 2 n 10 and 02 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 21 TheBinomialDistributionShape n 5 0 1 0 2 4 6 0 1 2 3 4 5 X P X n 5 0 5 2 4 6 0 1 2 3 4 5 X P X 0 Theshapeofthebinomialdistributiondependsonthevaluesof andn Here n 5and 1 Here n 5and 5 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 22 TheBinomialDistributionUsingBinomialTables Examples n 10 35 x 3 P x 3 n 10 35 2522n 10 75 x 2 P x 2 n 10 75 0004 BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 23 BinomialDistributionCharacteristics Mean VarianceandStandardDeviation Wheren samplesize probabilityoftheeventofinterestforanytrial 1 probabilityofnoeventofinterestforanytrial BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 24 TheBinomialDistributionCharacteristics n 5 0 1 0 2 4 6 0 1 2 3 4 5 X P X n 5 0 5 2 4 6 0 1 2 3 4 5 X P X 0 Examples BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 25 UsingExcelForTheBinomialDistribution BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 26 ThePoissonDistributionDefinitions YouusethePoissondistributionwhenyouareinterestedinthenumberoftimesaneventoccursinagivenareaofopportunity Anareaofopportunityisacontinuousunitorintervaloftime volume orsuchareainwhichmorethanoneoccurrenceofaneventcanoccur Thenumberofscratchesinacar spaintThenumberofmosquitobitesonapersonThenumberofcomputercrashesinaday BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 27 ThePoissonDistribution ApplythePoissonDistributionwhen YouwishtocountthenumberoftimesaneventoccursinagivenareaofopportunityTheprobabilitythataneventoccursinoneareaofopportunityisthesameforallareasofopportunityThenumberofeventsthatoccurinoneareaofopportunityisindependentofthenumberofeventsthatoccurintheotherareasofopportunityTheprobabilitythattwoormoreeventsoccurinanareaofopportunityapproacheszeroastheareaofopportunitybecomessmallerTheaveragenumberofeventsperunitis lambda BusinessStatistics AFirstCourse 5e 2009Prentice Hall Inc Chap5 28 PoissonDistributionFormula where X numberofeventsinanareaofopportunity expectednumberofeventse