概率论基础教程
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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作者简介
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。1968年博士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Simulation（《统计模拟》）、Introduction to Probability Models（《应用随机过程：概率模型导论》）等（均由人民邮电出版社引进出版）。
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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
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