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
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
CHAPTER 8 Introduction to Linear Regression 396
8.1 The Method of Least Squares 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
CHAPTER 10 Linear Regression 494
10.1 Least-Squares Estimation 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
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