概率论基础教程（英文版·第8版）

　　《概率论基础教程（英文版·第8版）》是世界各国高校广泛采用的概率论教材，通过大量的例子讲述了概率论的基础知识，主要内容有组合分析、概率论公理化、条件概率和独立性、离散和连续型随机变量、随机变量的联合分布、期望的性质、极限定理等。《概率论基础教程（英文版·第8版）》附有大量的练习，分为习题、理论习题和自检习题三大类，其中自检习题部分还给出全部解答。《概率论基础教程（英文版·第8版）》适用于大专院校数学、统计、工程和相关专业（包括计算科学、生物、社会科学和管理科学）的学生阅读，也可供各学科专业科技人员参考。

　　罗斯，Sheldon M. Ross国际知名概率与统计学家，南加州大学工业工程与运筹系系主任。毕业于斯坦福大学统计系，曾在加州大学伯克利分校任教多年。研究领域包括：随机模型．仿真模拟、统计分析、金融数学等：Ross教授著述颇丰，他的多种畅销数学和统计教材均产生了世界性的影响，如Introduction to Probability Models（《应用随机过程：概率模型导论》），A First Course in Probability（《概率论墓础教程》）等（均由人民邮电出版社出版）。

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 BayessFormula
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 ChebyshevsInequalityandtheWeakLawofLargeNumbers
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