第七版 Indroduction_to_Mathematica_Statistics.Hogg,McKean,Craig seventh edition.pdf UIUC的 STAT401統(tǒng)計(jì)課程教材 Contents Preface ix 1 Probability and Distributions 1 1.1 Introduction................................ 1 1.2 SetTheory ................................ 3 1.3 TheProbabilitySetFunction ...................... 10 1.4 ConditionalProbabilityandIndependence . . . . . . . . . . . . . . . 21 1.5 RandomVariables ............................ 32 1.6 DiscreteRandomVariables ....................... 40 1.6.1 Transformations ......................... 42 1.7 ContinuousRandomVariables...................... 44 1.7.1 Transformations ......................... 46 1.8 ExpectationofaRandomVariable ................... 52 1.9 SomeSpecialExpectations ....................... 57 1.10ImportantInequalities .......................... 68 2 Multivariate Distributions 73 2.1 DistributionsofTwoRandomVariables ................ 73 2.1.1 Expectation............................ 79 2.2 Transformations: Bivariate Random Variables . . . . . . . . . . . . . 84 2.3 Conditional Distributions and Expectations . . . . . . . . . . . . . . 94 2.4 TheCorrelationCoefficient ....................... 102 2.5 IndependentRandomVariables.....................110 2.6 ExtensiontoSeveralRandomVariables . . . . . . . . . . . . . . . . 117 2.6.1 ?Multivariate Variance-Covariance Matrix . . . . . . . . . . . 123 2.7 Transformations for Several Random Variables . . . . . . . . . . . . 126 2.8 LinearCombinationsofRandomVariables. . . . . . . . . . . . . . . 134 3 Some Special Distributions 139 3.1 TheBinomialandRelatedDistributions . . . . . . . . . . . . . . . . 139 3.2 ThePoissonDistribution ........................ 150 3.3 TheΓ,χ2,andβDistributions ..................... 156 3.4 TheNormalDistribution......................... 168 3.4.1 ContaminatedNormals ..................... 174 v vi Contents ?3.5 TheMultivariateNormalDistribution ................. 178 3.5.1 ?Applications........................... 185 3.6 t-andF-Distributions