TEST BANK FOR Probability and Statistics Fourth edition by Morris H. DeGroot , Mark J. Schervish ISBN:978-0321500465 ALL CHAPTERS COVERED YOUR ULTIMATE GUIDE 100% VERIFIED A+ GRADE ASSURED!!!!! NEW LATEST UPDATE!!!!!!

INSTRUCTOR’S SOLU GT




TIONS MANUAL (ONLI
GT GT




NE ONLY)
GT




MARK SCHERVISHGT




Carnegie Mellon University
GT GT




P ROBABILITY AND STATISTICS
G T G T




FOURTH EDITION GT




Morris DeGroot GT



Carnegie Mellon University
GT GT




Mark Schervish
GT



Carnegie Mellon University
GT GT

,TheGTauthorGTandGTpublisherGTofGTthisGTbookGThaveGTusedGTtheirGTbestGTeffortsGTinGTpreparingGTthisGTbook.GTTheseGTef
fortsGTincludeGTtheGTdevelopment, GTresearch,GTandGTtestingGTofGTtheGTtheoriesGTandGTprogramsGTtoGTdetermineGTtheirGT
effectiveness. GTTheGTauthorGTandGTpublisherGTmakeGTnoGTwarrantyGTofGTanyGTkind,GTexpressedGTorGTimplied, GTwithGTre
gardGTtoGTtheseGTprogramsGTorGTtheGTdocumentationGTcontainedGTinGTthisGTbook.GTTheGTauthorGTandGTpublisherGTshallG
Tnot GT beGTliableGTin GT any GT event GT forGTincidental GT orGT consequential GT damages GT in GT connection GT with, GT orGT arising GT o

utGTof,GTtheGTfurnishing, GTperformance, GTorGTuseGTofGTtheseGTprograms.

ReproducedGTbyGTPearsonGTAddison-

WesleyGTfromGTelectronicGTfilesGTsuppliedGTbyGTtheGTauthor.GTCopyrightGT©GT2012,GT200

2,GT1986GTPearsonGTEducation,GTInc.
PublishingGTasGTPearson GTAddison-Wesley,GT75GTArlingtonGTStreet,GTBoston,GTMAGT02116.

AllGTrightsGTreserved.GTThisGTmanualGTmayGTbeGTreproducedGTforGTclassroom

GTuseGTonly.GTISBN-13:GT978-0-321-71597-5
ISBN-10:G T 0-321-71597-7

,Contents

Preface .................................................................................................................................................................... vi

1 IntroductionGTtoGTProbability 1
1.2 InterpretationsG T ofG T ProbabilityG T G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .
G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 1
1.4 SetG T TheoryG T G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G
T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 1
1.5 TheG T DefinitionG T ofG T ProbabilityG T G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .
G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 3
1.6 FiniteG T SampleG T SpacesG T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .
G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 6
1.7 CountingG T MethodsG T G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G
T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 7
1.8 CombinatorialG T MethodsG T G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G
T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T .G T . 8
1.9 MultinomialG T Coefficients ...........................................................................................................................13
1.10 TheGTProbabilityGT ofGTaGTUnionGTofGTEvents .............................................................................................. 16
1.12G T SupplementaryG T Exercises .........................................................................................................................20

2 ConditionalG T Probability 25
2.2 TheG T DefinitionG T ofG T ConditionalG T Probability .........................................................................................25
2.3 IndependentG T Events ....................................................................................................................................28
2.4 Bayes’G T Theorem ..........................................................................................................................................34
2.5 TheG T Gambler’sG T RuinG T Problem ..............................................................................................................40
2.6 SupplementaryG T Exercises ...........................................................................................................................41

3 RandomG T VariablesG T andG T Distributions 49
3.2 RandomGTVariablesGTandGTDiscreteGTDistributions ................................................................................... 49
3.3 ContinuousG T Distributions ............................................................................................................................50
3.4 TheGTCumulativeGT DistributionGTFunction ................................................................................................ 53
3.5 BivariateGTDistributions.............................................................................................................................. 58
3.6 MarginalGTDistributions ............................................................................................................................... 64
3.7 ConditionalG T Distributions ......................................................................................................................... 70
3.8 MultivariateG T Distributions........................................................................................................................ 76
3.9 FunctionsG T ofG T aG T RandomG T Variable .........................................................................................................81
3.10 FunctionsG T ofG T TwoG T orG T MoreG T RandomG T Variables ...............................................................................85
3.11 MarkovGTChains ........................................................................................................................................... 93
3.12 SupplementaryG T Exercises ...........................................................................................................................97

4 Expectation 107
CopyrightGT©GT2012GTPearsonGTEducation,GTInc.G T PublishingGTasGTAddison
-Wesley.

, 4.2 TheGTExpectationGT ofGTaGTRandomGTVariable .......................................................................................... 107
4.3 PropertiesG T ofG T Expectations ...................................................................................................................... 110
4.4 Variance ....................................................................................................................................................... 113
4.5 Moments...................................................................................................................................................... 115
4.6 TheG T MeanG T andG T theG T Median ................................................................................................................ 118

4.7 CovarianceG T andG T Correlation.................................................................................................................... 121
4.8 ConditionalG T Expectation ......................................................................................................................... 124
4.9 Utility.......................................................................................................................................................... 129
4.10 SupplementaryG T Exercises ......................................................................................................................... 134

5 SpecialG T Distributions 141
5.2 TheGTBernoulliGT andGT BinomialGT Distributions ....................................................................................... 141
5.3 TheG T HypergeometricG T Distributions........................................................................................................ 145
5.4 TheGTPoissonGTDistributions ..................................................................................................................... 149
5.5 TheGTNegativeGTBinomialGTDistributions .................................................................................................. 155
5.6 TheGT NormalGT Distributions ..................................................................................................................... 159
5.7 TheGT GammaGT Distributions .................................................................................................................... 165
5.8 TheG T BetaG T Distributions .......................................................................................................................... 171
5.9 TheGTMultinomialGTDistributions ............................................................................................................. 174
5.10 TheGTBivariateGT NormalGTDistributions .................................................................................................... 177
5.11 SupplementaryG T Exercises ......................................................................................................................... 182

6 LargeG T RandomG T Samples 187
6.2 Introduction ................................................................................................................................................. 187
6.3 TheGT LawG T ofG T LargeG T Numbers .............................................................................................................. 188
6.4 TheG T CentralG T LimitG T Theorem .............................................................................................................. 194
6.5 TheG T CorrectionG T forG T Continuity ............................................................................................................. 198
6.6 SupplementaryG T Exercises ......................................................................................................................... 199

7 Estimation 203
7.2 StatisticalG T Inference ................................................................................................................................. 203
7.3 PriorGTandGTPosteriorGTDistributions ......................................................................................................... 204
7.4 ConjugateGTPriorGTDistributions .............................................................................................................. 207
7.5 BayesG T Estimators ....................................................................................................................................... 214
7.6 MaximumG T LikelihoodG T Estimators ......................................................................................................... 217
7.7 PropertiesG T ofG T MaximumG T LikelihoodG T Estimators .............................................................................. 220
7.8 SufficientG T Statistics .................................................................................................................................... 225
7.9 JointlyGTSufficientGTStatistics ..................................................................................................................... 228
7.10 ImprovingGTanGTEstimator......................................................................................................................... 230
7.11 SupplementaryG T Exercises ......................................................................................................................... 234

8 SamplingG T DistributionsG T ofG T Estimators 239
8.2 TheGTSamplingGTDistributionGT ofGT aGTStatistic ......................................................................................... 239
8.3 TheG T Chi-SquareG T Distributions ............................................................................................................... 241
8.4 JointGTDistributionGTofGTtheGTSampleGTMeanGTandGTSampleGTVariance .................................................. 245
8.5 TheG T tG T Distributions ................................................................................................................................ 247
8.6 ConfidenceG T Intervals ................................................................................................................................. 250
8.7 BayesianGT Analysis GT ofGTSamplesGTfromGTaGT NormalGT Distribution ........................................................ 254
Copyright GT©GT2012GTPearsonGTEducation,GTInc.G T PublishingGTasGTAddison

-Wesley.