概率论基础教程
概率论基础教程封面图

概率论基础教程

(美) 罗斯 (Ross,S.M.) , 著

出版社:人民邮电出版社

年代:2009

定价:69.0

书籍简介:

本书主要内容有组合分析、概率论公理化、条件概率和独立性、随机变量的联合分布、期望的性质、极限定理等。

作者介绍:

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)。

书籍目录:

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 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

内容摘要:

《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。

编辑推荐:

《概率论基础教程(英文版·第8版)》叙述清晰、例子丰富,内容的选取不仅适合学生的兴趣,还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。《概率论基础教程(英文版·第8版)》还附有大量的练习,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,有利于巩固和自测所学知识。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。而这本经典的概率论教材,在世界各国的概率论教学中,也发挥着举足轻重的作用,据统计,在全球高校采用率最高。它初版于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。

书籍规格:

书籍详细信息
书名概率论基础教程站内查询相似图书
丛书名图灵原版数学
9787115209542
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出版地北京出版单位人民邮电出版社
版次1版印次1
定价(元)69.0语种英文
尺寸26装帧平装
页数 272 印数 2500

书籍信息归属:

概率论基础教程是人民邮电出版社于2009.07出版的中图分类号为 O211 的主题关于 概率论-教材-英文 的书籍。