概率与统计推断（英文版）WILEY
作者：
Robert Bartoszynski

Magdalena Niewiadomska-Bugaj



CONTENTS
X
Preface
1
1  Experiments, Sample Spaces, and Events
1
1.1  Introduction
2
1.2  Sample Space
9
1.3  Algebra of Events
16
1.4  Infinite Operations on Events
25
Probability
25
2.1  Introduction
25
2.2  Probability as a Frequency
26
2.3  Axioms of Probability
31
2.4  Consequences of the Axioms
36
2.5  Classical Probability
37
2.6  Necessity of the Axioms*
42
2.7  Subjective Probability*
V
vi  CONTENTS
3  Counting  47
3.1  Introduction  47
3.2  Product Sets, Orderings, and Permutations  47
3.3  Binomial Coefficients  55
3.4  Extension of Newton’s Formula  68
3.5  hlultinomial Coefficients  69
4  Conditional Probability: Independence  73
4.1  Introduction  73
4.2  Conditional Probability  74
4.3  Partitions; Total Probability Formula  80
4.4  Bayes’ Formula  87
4.5  Independence  92
4.6  Exchangeability; Conditional Independence  99
5  Markov Chains*  103
5.1  Introduction and Basic Definitions  103
5.2  Definition of a Markov Chain  106
5.3  n-Step Transition Probabilities  111
5.4  The Ergodic Theorem  114
5.5  Absorption Probabilities  122
6  Random Variables: Univariate Case  125
6.1  Introduction  125
6.2  Distributions of Random Variables  126
6.3  Discrete and Continuous Random Variables  139
6.4  Functions of Random Variables  150
6.5  Survival and Hazard Functions  157
7  Random Variables: Multivariate Case  161
7.1  Bivariate Distributions  161
7.2  Marginal Distributions; Independence  168
7.3  Conditional Distributions  180
7.4  Bivariate Transformations  187
7.5  Multidimensional Distributions  196
8  Expectation  203
8.1  Introduction  203
8.2  Expected Value  204
CONTENTS  vii
8.3  Expectation as an Integral*  212
8.4  Properties of Expectation  220
8.5  Moments  228
8.6  Variance  236
8.7  Conditional Expectation  248
8.8  Inequalities  252
9  Selected Families of Distributions  257
9.1  Bernoulli Trials and Related Distributions  257
9.2  Hypergeometric  Distribution  2 70
9.3  Poisson Distribution and Poisson Process  2 76
9.4  Exponential, Gamma and Related Distributions  290
9.5  Normal Distribution  296
9.6  Beta Distribution  306
10  Random Samples  311
10.1  Statistics and their Distributions  311
10.2  Distributions Related to Normal  313
10.3  Order Statistics  319
10.4  Generating Random Samples  325
10.5  Convergence  330
10.6  Central Limit Theorem  342
11  Introduction to Statistical Inference  351
11.1  Overview  351
11.2  Descriptive Statistics  353
11.3  Basic Model  358
11.4  Bayesian Statistics  360
11.5  Sampling  360
11.6  Measurement  Scales  367
12  Estimation  373
12.1  Introduction  373
12.2  Consistency  378
12.3  Loss, Risk, and Admissibility  381
12.4  Efficiency  386
12.5  Methods of Obtaining Estimators  394
12.6  Sufficiency  424
12.7  Interval Estimation  440
viii  CONTENTS
13  Testing Statistical Hypotheses  455
13.1  Introduction  455
13.2  Intuitive Background  460
13.3  Most Powerful Tests  469
13.4  Uniformly Most Powerful Tests  48 1
13.5  Unbiased Tests  487
13.6  Generalized Likelihood Ratio Tests  491
13.7  Conditional Tests  498
13.8  Tests and Confidence Intervals  501
13.9  Review of Tests for Normal Distributions  502
13.10  Monte Carlo, Bootstrap, and Permutation Tests  512
14  Linear Models  517
14.1  Introduction  517
14.2  Regression of the First and Second Kind  519
14.3  Distributional Assumptions  525
14.4  Linear Regression in the Normal Case  528
14.5  Testing Linearity  535
14.6  Prediction  538
14.7  Inverse Regression  540
14.8  BLUE  542
14.9  Regression Toward the Mean  545
14.10  Analysis of Variance  546
14.11  One-way Layout  547
14.12  Two-way Layout  550
14.13  ANOVA Models with Interaction  553
14.14  Further Extensions  557
15  Rank Methods  559
15.1  Introduction  559
15.2  Glivenko-Cantelli Theorem  560
15.3  Kolmogorov-Smirnov Tests  564
15.4  One-Sample Rank Tests  571
15.5  Two-Sample Rank Tests  578
15.6  Kruskal-Wallis Test  582
16  Analysis of Categorical Data  585
16.1  Introduction  585
16.2  Chi-square Tests  587
CONTENTS  ix
16.3  Homogeneity and Independence  593
16.4  Consistency and Power  599
16.5  2x2 Contingency Tables  604
16.6  r x c Contingency Tables  612
Statistical Tables  617
Bibliography  629
Answers to Odd-Numbered  Problems  634
Index  642