概率论基础教程

图书标准信息

• 作者 [美]罗斯 著
• 出版社 人民邮电出版社
• 出版时间 2009-07
• 版次 1
• ISBN 9787115209542
• 定价 69.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 530页
• 字数 648千字
• 正文语种 英语
• 丛书 图灵原版数学·统计学系列

【内容简介】

　　《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。

【作者简介】

　　罗斯，SheldonM.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IntroductiontoProbabilityModels（《应用随机过程：概率模型导论》），AFirstCourseinProbability（《概率论墓础教程》）等（均由人民邮电出版社出版）。

【目录】

1CombinatorialAnalysis
1.1Introduction
1.2TheBasicPrincipleofCounting
1.3Permutations
1.4Combinations
1.5MultinomialCoefficients
1.6TheNumberofIntegerSolutlonsofEquations
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

2AxiomsofProbability
2.1Introduction
2.2SampleSpaceandEvents
2.3AxiomsofProbability
2.4SomeSimplePropositions
2.5SampleSpaceHavingEquallyLikelyOutcomes33
2.6ProbabilityasaContinuousSetFunction
2.7ProbabilityasaMeasureofBelief
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

3ConditionalProbabilityandIndependence
3.1Introduction
3.2ConditionalProbabilities
3.3BayessFormula
3.4IndependentEvents
3.5P(·|F)IsaProbability
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

4RandomVariables
4.1RandomVariables
4.2DiscreteRandomVariables
4.3ExpectedValue
4.4ExpectationofaFunctionofaRandomVariable
4.5Variance
4.6TheBernoulhandBinomialRandomVariables
4.6.1PropertiesofBinomialRandomVariables
4.6.2ComputingtheBinomialDistributionFunction
4.7ThePoissonRandomVariable
4.7.1ComputingthePoissonDistributionFunction
4.8OtherDiscreteProbabilityDistributions
4.8.1TheGeometricRandomVariable
4.8.2TheNegativeBinomialRandomVariable
4.8.3TheHypergeometricRandomVariable
4.8.4TheZeta(orZipf)Distribution
4.9ExpectedValueofSumsofRandomVariables
4.10PropertiesoftheCumulativeDistributionFunction
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

5ContinuousRandomVariables
51Introduction
5.2ExpectationandVarianceofContinuousRandomVariables
5.3TheUniformRandomVariable
5.4NormalRandomVariables
5.4.1TheNormalApproximationtotheBinomialDistribution
5.5ExponentialRandomVariables
5.5.1HazardRateFunctions
5.6OtherContinuousDistributions
5.6.1TheGammaDlstrlbutlon
5.6.2TheWeibullDlStrlbutlon
5.6.3TheCauchyDistribution
5.6.4TheBetaDlStrlbutlon
5.7TheDistributionofaFunctionofaRandomVariable
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

6JointlyDistributedRandomVariables
6.1JointDistributionFunctions
6.2IndependentRandomVariables
6.3SumsofIndependentRandomVariables
6.3.1IdenticallyDistributedUniformRandomVariables
6.3.2GammaRandomVariables
6.3.3NormalRandomVariables
6.3.4PolssonandBinomialRandomVariables
635GeometricRandomVariables
6.4ConditionalDistribution：DiscreteCase
6.5ConditionalDistribution：ContinuousCase
66OrderStatistics
6.7JointProbabilityDistributionofFunctionsofRandomVariables
6.8ExciaanzeaoleRandomVariables
Summary
Problems
TheoreticalExercises
SelfTestProblemsandExercises

7PropertiesofExpectation
7.1Introduction
7.2ExpectationofSumsofRandomVariablviatheProbabilisticMethod
7.2.2TheMaximum-MinimumsIdentity
7.3MomentsoftheNumberofEventsthatOccur
7.4Covariance，VarianceofSums，andCorrelations
7.5ConditionalExpectation
7.5.1Definitions
7.5.2ComputingExpectationsbyConditioning
7.5.3ComputingProbabilitiesbyConditioning
7.5.4ConditionalVariance
7.6ConditionalExpectationandPrediction
7.7MomentGeneratingFunctions
7.7.1JointMomentGeneratingFunctions
7.8AddltlonaproprietariesofNormalRandomVariables
7.8.1TheMultivariateNormalDlstrlbution
7.8.2TheJointDistributionoftheSampleMeanandSampleVariance
7.9GeneralDefinitionofExpectation
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

8LimitTheorems
8.1Introduction
8.2ChebyshevsInequalityandtheWeakLawofLargeNumbers
8.3TheCentralLimitTheorem
8.4TheStrongLawofLargeNumbers
8.5OtherInequamles
8.6BoundingtheErrorProbabilityWhenApproximatingaSumofIndependentBernoulliRandomVariablesbyaPoissonRandomVariable
Summary
Problems
TheoreticalExercises
Self-TestProblemsandExercises

9AdditionalTopicsinProbability
9.1ThePoissonProcess
9.2MarkovChains
9.3Surprise，Uncertainty，andEntropy
9.4CodingTheoryandEntropy
Summary
ProblemsandTheoreticalExercises
Self-TestProblemsandExercises
References

10Simulation
10.1Introduction
10.2GeneralTechniquesforSimulatingContinuousRandomVariables
10.2.1TheInverseTransformationMethod
10.2.2TheRejectionMethod
10.3SimulatingfromDiscreteDistributions
10.4VarianceReductionTechniques
10.4.1UseofAntitheticVariables
10.4.2VarianceReductionbyConditioning
10.4.3ControlVariates
Summary
Problems
Self-TestProblemsandExercises
Reference

AnswerstoSelectedProblems
SolutionstoSelf-TestProblemsandExercises
Index