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第七版 Indroduction_to_Mathematica_Statistics.Hogg,McKean,Craig seventh edition.pdf UIUC的 STAT401统计课程教材 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

Although many books have been written about Mathematica, very few of them cover the new functionality added to the most recent versions of the program. Mathematica Beyond Mathematics: The Wolfram Language in the Real World introduces the new features using real-world examples, based on the experience of the author as a consultant. In the process, you will also learn more about the Wolfram Language and how you can use it to solve a wide variety of problems. The author raises questions from a wide range of topics and answers them by taking full advantage of Mathematicas latest features. For example What sources of energy does the world really use? How can we calculate tolerance limits in manufacturing processes? Are our cities getting warmer? Is the novel El Quijote written in Pi? How can we find planets outside our solar system?

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