概率论讲义
￥ 29 5.9折 ￥ 49 九五品
仅1件
作者魏舟 著
出版社科学出版社
ISBN9787030695161
出版时间2021-08
版次1
装帧平装
开本16开
纸张胶版纸
页数141页
字数99999千字
定价49元
上书时间2024-03-30
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基本信息
书名:概率论讲义
定价：49.00元
作者:魏舟 著
出版社：科学出版社
出版日期：2021-08-01
ISBN：9787030695161
字数：165000
页码：141
版次：
装帧：平装
开本：16开
商品重量：
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内容提要
《概率论讲义=Lecture Notes oProbability Theory：英文》是全英文撰写，共六章，内容包括：概率及概率空间，随机变量及分布函数，联合分布随机变量，随机变量的期望与方差，随机变量的特征函数，大数定律与中心极限定理。《概率论讲义=Lecture Notes oProbability Theory：英文》篇幅不大、内容精练，深入分析了知识点背后的数学本质，并给出了一些重要结论的详细数学证明。
目录
Contents 丛书序 序言 Preface Chapter 1 Probability and Probability Space 1 1.1 What is Probability? 1 1.2 Sample Space and Events 2 1.3 Definitioof Probability 4 1.3.1 Classic Probability 4 1.3.2 Empirical Probability 6 1.3.3 Geometrical Probability 7 1.4 Axioms of Probability and Probability Space 10 1.4.1 Algebra and σ-Algebra 10 1.4.2 Axioms of Probability 10 1.5 Conditional Probability 14 1.5.1 Definitioof Conditional Probability 14 1.5.2 Law of Total Probability and Bayes5 Formula 16 1.5.3 Independent Events 18 Chapter 2 Random Variables and DistributioFunctions 21 2.1 The DistributioFunctioof a Random Variable 21 2.2 Discrete Random Variables 24 2.2.1 Definitioof a Discrete Random Variable 24 2.2.2 The Bernoulli Random Variable 25 2.2.3 The PoissoRandom Variable 26 2.3 Continuous Random Variables 33 2.3.1 Definitioof a Continuous Random Variable 33 2.3.2 Normal Random Variable 34 2.3.3 Other Continuous Random Variables 36 Chapter 3 Jointly Distributed Random Variables 40 3.1 The Joint DistributioFunctio40 3.1.1 Jointly Distributed Discrete Random Variables 41 3.1.2 Jointly Distributed Continuous Random Variables 41 3.1.3 The Marginal Distributio42 3.2 Independent Random Variables 44 3.3 The Conditional Distributio46 3.3.1 The Jointly Distributed Discrete Random Variables Case 46 3.3.2 The Jointly Distributed Continuous Random Variables Case 47 3.4 The Joint Probability Distributioof Functions of Random Variables 48 3.4.1 Key Theorem 49 3.4.2 Transformations of Two Random Variables 50 Chapter 4 Expectatioand Variance of Random Variables 56 4.1 Expectatioand Variance of a Discrete Random Variable 56 4.2 Expectatioand Variance of a Continuous Random Variable 58 4.3 General Definitioof Expectatio61 4.4 Moments of a Random Variable 66 4.5 Geometric Property of Expectatio68 4.6 Expectatioof Jointly Distributed Random Variables 69 4.6.1 Two Dimensional Riemann-Stieltjes Integral 69 4.6.2 Covariance of Jointly Distributed Random Variables 71 4.6.3 Expectatioof Functions of Jointly Distributed Random Variables 73 4.6.4 Correlatio76 Chapter 5 Characteristic Functions of Random Variables 79 5.1 The Characteristic Functioof a Random Variable 79 5.2 The InversioFormula of the Characteristic Functio84 5.3 The Joint Characteristic Functio88 Chapter 6 Large Number Laws and Central Limit Theorem 93 6.1 Convergence iProbability Theory 93 6.2 Laws of Large Numbers 97 6.2.1 Weak Law of Large Numbers 97 6.2.2 Strong Law of Large Numbers 99 6.3 Central Limit Theorem 101 6.3.1 The Central Limit Theorem 101 6.3.2 Linderberg-Feller Theorem 105 6.4 Proofs of Theorems 5.1.2， 6.2.3 and 6.3.2 112 References 126 Appendix 1 Numerical Table for PoissoDistributio127 Appendix 2 Numerical Table for Standard Normal Distributio133 Appendix 3 Translatioof Some Mathematical Professional Terms (部分专业词汇对照表） 135 Appendix 4 Translatioof Some Mathematicians (译名对照表） 137 Index 138
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