www.it-ebooks.info www.it-ebooks.info Probability www.it-ebooks.info www.it-ebooks.info Probability An Introduction with Statistical Applications Second Edition John J. Kinney ColoradoSprings,CO www.it-ebooks.info Copyright©2015byJohnWiley&Sons,Inc.Allrightsreserved PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey PublishedsimultaneouslyinCanada Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyany means,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunder Section107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthe Publisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter, Inc.,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4470,oronthewebat www.copyright.com.RequeststothePublisherforpermissionshouldbeaddressedtothePermissions Department,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,(201)748-6011,fax(201) 748-6008,oronlineathttp://www.wiley.com/go/permissions. LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyorcompletenessof thecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesofmerchantabilityorfitnessfora particularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentativesorwrittensalesmaterials. Theadviceandstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwitha professionalwhereappropriate.Neitherthepublishernorauthorshallbeliableforanylossofprofitoranyother commercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orotherdamages. Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactourCustomer CareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat(317)572-3993orfax (317)572-4002. Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmaynotbe availableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteatwww.wiley.com. LibraryofCongressCataloging-in-PublicationData: Kinney,JohnJ. Probability:anintroductionwithstatisticalapplications/JohnKinney,ColoradoSprings, CO.–Secondedition. pagescm Includesbibliographicalreferencesandindex. ISBN978-1-118-94708-1(cloth) 1. Probabilities–Textbooks.2. Mathematicalstatistics–Textbooks. I.Title. QA273.K4932015 519.2–dc23 2014020218 PrintedintheUnitedStatesofAmerica 10987654321 www.it-ebooks.info Thisbookisfor CherryandKaylyn www.it-ebooks.info www.it-ebooks.info Contents PrefacefortheFirstEdition xi PrefacefortheSecondEdition xv 1. SampleSpacesandProbability 1 1.1. DiscreteSampleSpaces 1 1.2. Events;AxiomsofProbability 7 AxiomsofProbability 8 1.3. ProbabilityTheorems 10 1.4. ConditionalProbabilityandIndependence 14 Independence 23 1.5. SomeExamples 28 1.6. ReliabilityofSystems 34 SeriesSystems 34 ParallelSystems 35 1.7. CountingTechniques 39 ChapterReview 54 ProblemsforReview 56 SupplementaryExercisesforChapter1 56 2. DiscreteRandomVariablesandProbabilityDistributions 61 2.1. RandomVariables 61 2.2. DistributionFunctions 68 2.3. ExpectedValuesofDiscreteRandomVariables 72 ExpectedValueofaDiscreteRandomVariable 72 VarianceofaRandomVariable 75 Tchebycheff’sInequality 78 2.4. BinomialDistribution 81 2.5. ARecursion 82 TheMeanandVarianceoftheBinomial 84 2.6. SomeStatisticalConsiderations 88 2.7. HypothesisTesting:BinomialRandomVariables 92 2.8. DistributionofASampleProportion 98 2.9. GeometricandNegativeBinomialDistributions 102 ARecursion 108 2.10. TheHypergeometricRandomVariable:AcceptanceSampling 111 AcceptanceSampling 111 TheHypergeometricRandomVariable 114 SomeSpecificHypergeometricDistributions 116 2.11. AcceptanceSampling(Continued) 119 vii www.it-ebooks.info viii Contents Producer’sandConsumer’sRisks 121 AverageOutgoingQuality 122 DoubleSampling 124 2.12. TheHypergeometricRandomVariable:FurtherExamples 128 2.13. ThePoissonRandomVariable 130 MeanandVarianceofthePoisson 131 SomeComparisons 132 2.14. ThePoissonProcess 134 ChapterReview 139 ProblemsforReview 141 SupplementaryExercisesforChapter2 142 3. ContinuousRandomVariablesandProbabilityDistributions 146 3.1. Introduction 146 MeanandVariance 150 AWordonWords 153 3.2. UniformDistribution 157 3.3. ExponentialDistribution 159 MeanandVariance 160 DistributionFunction 161 3.4. Reliability 162 HazardRate 163 3.5. NormalDistribution 166 3.6. NormalApproximationtotheBinomialDistribution 175 3.7. GammaandChi-SquaredDistributions 178 3.8. WeibullDistribution 184 ChapterReview 186 ProblemsForReview 189 SupplementaryExercisesforChapter3 189 4. FunctionsofRandomVariables;GeneratingFunctions;Statistical Applications 194 4.1. Introduction 194 4.2. SomeExamplesofFunctionsofRandomVariables 195 4.3. ProbabilityDistributionsofFunctionsofRandomVariables 196 ExpectationofaFunctionofX 199 4.4. SumsofRandomVariablesI 203 4.5. GeneratingFunctions 207 4.6. SomePropertiesofGeneratingFunctions 211 4.7. ProbabilityGeneratingFunctionsforSomeSpecificProbabilityDistributions 213 BinomialDistribution 213 Poisson’sTrials 214 GeometricDistribution 215 CollectingPremiumsinCerealBoxes 216 4.8. MomentGeneratingFunctions 218 4.9. PropertiesofMomentGeneratingFunctions 223 4.10. SumsofRandomVariables–II 224 4.11. TheCentralLimitTheorem 229 4.12. WeakLawofLargeNumbers 233 4.13. SamplingDistributionoftheSampleVariance 234 www.it-ebooks.info