章节目录
1 CombinatorialAnalysis 1.1 Introduction 1.2 TheBasicPrincipleofCounting 1.3 Permutations 1.4 Combinations 1.5 MultinomialCoefficients 1.6 TheNumberofIntegerSolutlonsofEquations Summary Problems TheoreticalExercises Self-TestProblemsandExercises 2 AxiomsofProbability 2.1 Introduction 2.2 SampleSpaceandEvents 2.3 AxiomsofProbability 2.4 SomeSimplePropositions 2.5 SampleSpaceHavingEquallyLikelyOutcomes 33 2.6 ProbabilityasaContinuousSetFunction 2.7 ProbabilityasaMeasureofBelief Summary Problems TheoreticalExercises Self-TestProblemsandExercises 3 ConditionalProbabilityandIndependence 3.1 Introduction 3.2 ConditionalProbabilities 3.3 Bayes'sFormula 3.4 IndependentEvents 3.5 P(·|F)IsaProbability Summary Problems TheoreticalExercises Self-TestProblemsandExercises 4 RandomVariables 4.1 RandomVariables 4.2 DiscreteRandomVariables 4.3 ExpectedValue 4.4 ExpectationofaFunctionofaRandomVariable 4.5 Variance 4.6 TheBernoulhandBinomialRandomVariables 4.6.1 PropertiesofBinomialRandomVariables 4.6.2 ComputingtheBinomialDistributionFunction 4.7 ThePoissonRandomVariable 4.7.1 ComputingthePoissonDistributionFunction 4.8 OtherDiscreteProbabilityDistributions 4.8.1 TheGeometricRandomVariable 4.8.2 TheNegativeBinomialRandomVariable 4.8.3 TheHypergeometricRandomVariable 4.8.4 TheZeta(orZipf)Distribution 4.9 ExpectedValueofSumsofRandomVariables 4.10 PropertiesoftheCumulativeDistributionFunction Summary Problems TheoreticalExercises Self-TestProblemsandExercises 5 ContinuousRandomVariables 51 Introduction 5.2 ExpectationandVarianceofContinuousRandomVariables 5.3 TheUniformRandomVariable 5.4 NormalRandomVariables 5.4.1 TheNormalApproximationtotheBinomialDistribution 5.5 ExponentialRandomVariables 5.5.1 HazardRateFunctions 5.6 OtherContinuousDistributions 5.6.1 TheGammaDlstrlbutlon 5.6.2 TheWeibullDlStrlbutlon 5.6.3 TheCauchyDistribution 5.6.4 TheBetaDlStrlbutlon 5.7 TheDistributionofaFunctionofaRandomVariable Summary Problems TheoreticalExercises Self-TestProblemsandExercises 6 JointlyDistributedRandomVariables 6.1 JointDistributionFunctions 6.2 IndependentRandomVariables 6.3 SumsofIndependentRandomVariables 6.3.1 IdenticallyDistributedUniformRandomVariables 6.3.2 GammaRandomVariables 6.3.3 NormalRandomVariables 6.3.4 PolssonandBinomialRandomVariables 635 GeometricRandomVariables 6.4 ConditionalDistribution：DiscreteCase 6.5 ConditionalDistribution：ContinuousCase 66 OrderStatistics 6.7 JointProbabilityDistributionofFunctionsofRandomVariables 6.8 ExciaanzeaoleRandomVariables Summary Problems TheoreticalExercises SelfTestProblemsandExercises 7 PropertiesofExpectation 7.1 Introduction 7.2 ExpectationofSumsofRandomVariablviatheProbabilisticMethod 7.2.2 TheMaximum-MinimumsIdentity 7.3 MomentsoftheNumberofEventsthatOccur 7.4 Covariance,VarianceofSums,andCorrelations 7.5 ConditionalExpectation 7.5.1 Definitions 7.5.2 ComputingExpectationsbyConditioning 7.5.3 ComputingProbabilitiesbyConditioning 7.5.4 ConditionalVariance 7.6 ConditionalExpectationandPrediction 7.7 MomentGeneratingFunctions 7.7.1 JointMomentGeneratingFunctions 7.8 AddltlonaproprietariesofNormalRandomVariables 7.8.1 TheMultivariateNormalDlstrlbution 7.8.2 TheJointDistributionoftheSampleMeanandSampleVariance 7.9 GeneralDefinitionofExpectation Summary Problems TheoreticalExercises Self-TestProblemsandExercises 8 LimitTheorems 8.1 Introduction 8.2 Chebyshev'sInequalityandtheWeakLawofLargeNumbers 8.3 TheCentralLimitTheorem 8.4 TheStrongLawofLargeNumbers 8.5 OtherInequamles 8.6 BoundingtheErrorProbabilityWhenApproximatingaSumofIndependentBernoulliRandomVariablesbyaPoissonRandomVariable Summary Problems TheoreticalExercises Self-TestProblemsandExercises 9 AdditionalTopicsinProbability 9.1 ThePoissonProcess 9.2 MarkovChains 9.3 Surprise,Uncertainty,andEntropy 9.4 CodingTheoryandEntropy Summary ProblemsandTheoreticalExercises Self-TestProblemsandExercises References 10 Simulation 10.1 Introduction 10.2 GeneralTechniquesforSimulatingContinuousRandomVariables 10.2.1 TheInverseTransformationMethod 10.2.2 TheRejectionMethod 10.3 SimulatingfromDiscreteDistributions 10.4 VarianceReductionTechniques 10.4.1 UseofAntitheticVariables 10.4.2 VarianceReductionbyConditioning 10.4.3 ControlVariates Summary Problems Self-TestProblemsandExercises Reference AnswerstoSelectedProblems SolutionstoSelf-TestProblemsandExercises Index
内容简介
概率论作为数学的一个重要分支，在众多领域发挥着越来越突出的作用。本书是全球高校采用率最高的概率论教材之一，初版于1976年，多年来不断重印修订，是作者几十年教学和研究经验的结晶。 本书叙述清晰，例子丰富，特别针对学生的兴趣选取了内容，有助于学生建立概率直觉。第8版与时俱进，增加了很多新的习题和例子，并新增两节内容，分别推导具有均匀分布和几何分布的随机变量和的分布。本书还附有大量习题、理论习题和自检习题，其中自检习题部分还给出全部解答，有利于巩固和自测所学知识。
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