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PROBABILITY AND STOCHASTIC PROCESSESE2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

张丽华，周清主编著
出版社：北京：北京邮电大学出版社
ISBN：9787563545377
出版时间：2016
标注页数：324页
文件大小：79MB
文件页数：334页
主题词：概率论－高等学校－教材；随机过程－高等学校－教材

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图书目录

Chapter 1 Events and Their Probabilities1

1.1 The History of Probability1

1.2 Experiment,Sample Space and Random Event3

1.2.1 Basic Definitions3

1.2.2 Events as Sets5

1.3 Probabilities Defined on Events8

1.3.1 Classical Probability8

1.3.2 Geometric Probability13

1.3.3 The Frequency Interpretation of Probability16

1.4 Probability Space18

1.4.1 Axiomatic Definition of Probability19

1.4.2 Properties of Probability20

1.5 Conditional Probabilities24

1.5.1 The Definition of Conditional Probability24

1.5.2 The Multiplication Rule28

1.5.3 Total Probability Formula29

1.5.4 Bayes'Theorem32

1.6 Independence of Events36

1.6.1 Independence of Two Events36

1.6.2 Independence of Several Events40

1.6.3 Bernoulli Trials43

1.7 Review44

1.8 Exereises45

Chapter 2 Random Variable54

2.1 The Definition of a Random Variable54

2.2 The Distribution Function of a Random Variable56

2.2.1 The Definition and Properties of Distribution Function57

2.2.2 The Distribution Function of Function of a Random Variable67

2.3 Mathematical Expectation and Variance71

2.3.1 Expectation of a Random Variable71

2.3.2 Expectation of Functions of a Random Variable77

2.3.3 Variance of a Random Variable80

2.3.4 The Application of Expectation and Variation85

2.4 Discrete Random Variables87

2.4.1 Binomial Distribution with Parameters n and p87

2.4.2 Geometric Distribution92

2.4.3 Poisson Distribution with Parameters λ95

2.5 Continuous Random Variables98

2.5.1 Uniform Distribution98

2.5.2 Exponential Distribution102

2.5.3 Normal Distribution107

2.6 Review114

2.7 Exercises117

Chapter 3 Random Vectors126

3.1 Random Vectors and Joint Distributions126

3.1.1 Random Vectors and Joint Distributions127

3.1.2 Discrete Random Vectors129

3.1.3 Continuous Random Vectors134

3.2 Independence of Random Variables141

3.3 Conditional Distributions148

3.3.1 Discrete Case148

3.3.2 Continuous Case150

3.4 One Function of Two Random Variables153

3.4.1 Discrete Case153

3.4.2 Continuous case157

3.5 Transformation of Two Random Variables164

3.6 Numerical Characteristics of Random Vectors167

3.6.1 Expectation of Sums and Products167

3.6.2 Covariance and Correlation171

3.7 Multivariate Distributions178

3.7.1 Distribution Functions of Multiple Random Vectors178

3.7.2 Numerical Characteristics of Random Vectors181

3.7.3 Multiple Normal Distribution186

3.8 Review188

3.9 Exercises191

Chapter 4 Sequences of Random Variables200

4.1 Family of Distribution Functions and Numerical Characteristics201

4.2 Modes of Convergence204

4.3 The Law of Large Numbers207

4.4 The Central Limit Theorem210

4.5 Review213

4.6 Exercises214

Chapter 5 Introduction to Stochastic Processes218

5.1 Definition and Classification218

5.2 The Distribution Family and the Moment Functions222

5.3 The Moments of the Stochastic Processes223

5.3.1 Mean.Autocorrelation and Autocovariance223

5.3.2 Cross-correlation and Cross-covariance227

5.4 Stochastic Analysis228

5.5 Review231

5.6 Exercises231

Chapter 6 Stationary Processes233

6.1 Stationary Processes233

6.1.1 Strict Stationary Processes233

6.1.2 Wide Stationary Processes235

6.1.3 Joint Stationary Processes239

6.2 Ergodicity of Stationary Processes241

6.3 Power Spectral Density of Stationary Processes245

6.3.1 Average Power and Power Spectral Density245

6.3.2 Power Spectral Density and Autocorrelation Function248

6.3.3 Cross-Power Spectral Density251

6.4 Stationary Processes and Linear Systems253

6.5 Review258

6.6 Exercises259

Chapter 7 Finite Markov Chains262

7.1 Basic Concepts262

7.2 Markov Chains Having Two States267

7.3 Higher Order Transition Probabilities and Distributions272

7.4 Invariant Distributions and Ergodic Markov Chain279

7.5 How Does Google Work？285

7.6 Review289

7.7 Exercises290

Chapter 8 Independent-Increment Processes296

8.1 Independent-Increment Processes296

8.2 Poisson Process297

8.3 Gaussian Processes304

8.4 Brownian Motion and Wiener Processes307

8.5 Review310

8.6 Exercises311

Bibliography315

Appendix317

Table of Binomial Cofficients317

Table of Binomial Probabilities318

Table of Poisson Probabilities320

Table of Normal Probabilities323