概率统计 英文版PDF电子书下载

CHAPTER 1 Random Variables and Their Distributions 1

1.1 Introduction 1

1.2 Sample Distributions 5

1.3 Distributions 14

1.4 Random Variables 23

1.5 Probability Functions and Density Functions 33

1.6 Distribution Functions and Quantiles 45

1.7 Univariate Transformations 60

1.8 Independence 69

CHAPTER 2 Expectation 81

2.1 Introduction 81

2.2 Properties of Expectation 91

2.3 Variance 99

2.4 Weak Law of Large Numbers 110

2.5 Simulation and the Monte Carlo Method 121

CHAPTER 3 Special Continuous Models 134

3.1 Gamma and Beta Distributions 134

3.2 The Normal Distribution 145

3.3 Normal Approximation and the Central Limit Theorem 156

CHAPTER 4 Special Discrete Models 162

4.1 Combinatorics 162

4.2 The Binomial Distribution 172

4.3 The Multinomial Distribution 188

4.4 The Poisson Distribution 195

4.5 The Poisson Process 204

CHAPTER 5 Dependence 209

5.1 Covariance,Linear Prediction,and Correlation 209

5.2 Multivariate Expectation 219

5.3 Covariance and Variance-Covariance Matrices 225

5.4 Multiple Linear Prediction 236

5.5 Multivariate Density Functions 242

5.6 Invertible Transformations 252

5.7 The Multivariate Normal Distribution 263

CHAPTER 6 Conditioning 274

6.1 Conditional Distributions 274

6.2 Sampling Without Replacement 285

6.3 Hypergeometric Distribution 292

6.4 Conditional Density Functions 300

6.5 Conditional Expectation 307

6.6 Prediction 316

6.7 Conditioning and the Multivariate Normal Distribution 322

6.8 Random Parameters 330

CHAPTER 7 Normal Models 338

7.1 Introduction 338

7.2 Chi-Square,t,and F Distributions 344

7.3 Confidence Intervals 353

7.4 The t Test of an Inequality 365

7.5 The t Test of an Equality 375

7.6 The F Test 388

8.1 The Method of Least Squares 396

CHAPTER 8 Introduction to Linear Regression 396

8.2 Factorial Experiments 407

8.3 Input-Response and Experimental Models 415

CHAPTER 9 Linear Analysis 427

9.1 Linear Spaces 427

9.2 Identifiability 438

9.3 Saturated Spaces 447

9.4 Inner Products 454

9.5 Orthogonal Projections 470

9.6 Normal Equations 485

10.1 Least-Squares Estimation 494

CHAPTER 10 Linear Regression 494

10.2 Sums of Squares 506

10.3 Distribution Theory 515

10.4 Sugar Beet Experiment 526

10.5 Lube Oil Experiment 538

10.6 The t Test 552

10.7 Submodels 560

10.8 The F Test 568

CHAPTER 11 Orthogonal Arrays 579

11.1 Main Effects 579

11.2 Interactions 595

11.3 Experiments with Factors Having Three Levels 611

11.4 Randomization,Blocking,and Covariates 620

CHAPTER 12 Binomial and Poisson Models 635

12.1 Nominal Confidence Intervals and Tests 636

12.2 Exact P-Values 651

12.3 One-Parameter Exponential Families 662

CHAPTER 13 Logistic Regression and Poisson Regression 673

13.1 Input-Response and Experimental Models 675

13.2 Maximum-Likelihood Estimation 686

13.3 Existence and Uniqueness of the Maximum-Likelihood Estimate 699

13.4 Iteratively Reweighted Least-Squares Method 709

13.5 Normal Approximation 723

13.6 The Likelihood-Ratio Test 736

APPENDIX A Properties of Vectors and Matrices 751

APPENDIX B Summary of Probability 760

B.1 Random Variables and Their Distributions 760

B.2 Random Vectors 769

APPENDIX C Summary of Statistics 774

C.1 Normal Models 774

C.2 Linear Regression 779

C.3 Binomial and Poisson Models 785

C.4 Logistic Regression and Poisson Regression 787

APPENDIX D Hints and Answers 798

APPENDIX E Tables 828

Index 833