随机数学及其应用PDF电子书下载

Chapter 1 Events and Probability 1

1.1 Events as Sets 1

1.2 Probability 3

1.3 Exercises 32

Chapter 2 Random Variables and Their Distributions 36

2.1 Random Variables 36

2.2 Discrete Random Variables 39

2.3 Expected Value of Discrete Random Variable 39

2.4 Expectation of a Function of a Discrete Random Variable 40

2.5 Variance of Random Variables 43

2.6 Continuous Random Variables 60

2.7 Distribution of a Function of a Random Variable 72

2.8 Exercises 75

Chapter 3 Joint Distributions of Two Random Variables 79

3.1 Joint Cumulative Probability Distribution Function 79

3.2 Joint Probability Mass Function for Discrete Random Variable 80

3.3 Joint Probability Density Function 82

3.4 Independent Random Variables 85

3.5 Covariance 87

3.6 Correlation Coefficient 88

3.7 Bivariate Normal Distribution 94

3.8 Conditional Distributions 97

3.9 Joint Probability Distribution of Functions of Random Variables 116

3.10 Exercises 133

Chapter 4 Law of Large Numbers 139

4.1 Generating Functions and Their Applications 139

4.2 Characteristic Functions 151

4.3 Limit Theorems 156

4.4 Law of Large Numbers(LLN) 158

4.5 Exercises 177

Chapter 5 Mathematical Statistics 181

5.1 Introduction 181

5.2 Random Sampling 182

5.3 Distributions of Statistics 183

5.4 The Sample Mean and the Sample Variance 185

5.5 Point Estimation 188

5.6 Confidence Intervals 190

5.7 Testing of Hypotheses 191

5.8 Exercises 193

Chapter 6 Approaches to Semiparametric Bounds on Means and Variances 197

6.1 Introduction to Moment Problems 197

6.2 Convex Optimization Approach(Duality Theory) 200

6.3 Semidefinite Programming(SDP) 210

6.4 Khinchin Transform Method for Unimodal Distributions 213

6.5 Convex Representation 216

6.6 Symmetrization Methods for Variance 217

6.7 Optimal Distance and Optimal Ratio 233

6.8 Other Methods 234

Index 246

后记 248