Résumé
Updated classic statistics text, with new problems and examples
Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material.
In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition:
Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics
Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format
Offers students in statistics, mathematics, engineering and related fields a user-friendly resource
Provides practicing professionals valuable insight into statistical tools
Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.Preface vii
Preface vi
1 Experiments, Sample Spaces, and Events 1
1.1 Introduction 1
1.2 Sample Space 2
1.3 Algebra of Events 9
1.4 Infinite Operations on Events 15
2 Probability 25
2.1 Introduction 25
2.2 Probability as a Frequency 25
2.3 Axioms of Probability 26
2.4 Consequences of the Axioms 31
2.5 Classical Probability 35
2.6 Necessity of the Axioms* 36
2.7 Subjective Probability* 41
3 Counting 45
3.1 Introduction 45
3.2 Product Sets, Orderings, and Permutations 45
3.3 Binomial Coefficients 51
3.4 Multinomial Coefficients 64
4 Conditional Probability, Independence, and Markov Chains 67
4.1 Introduction 67
4.2 Conditional Probability 68
4.3 Partitions; Total Probability Formula 74
4.4 Bayes' Formula 79
4.5 Independence 84
4.6 Exchangeability; Conditional Independence 90
4.7 Markov Chains* 93
5 Random Variables: Univariate Case 107
5.1 Introduction 107
5.2 Distributions of Random Variables 108
5.3 Discrete and Continuous Random Variables 117
5.4 Functions of Random Variables 129
5.5 Survival and Hazard Functions 136
6 Random Variables: Multivariate Case 141
6.1 Bivariate Distributions 141
6.2 Marginal Distributions; Independence 148
6.3 Conditional Distributions 160
6.4 Bivariate Transformations 167
6.5 Multidimensional Distributions 176
7 Expectation 183
7.1 Introduction 183
7.2 Expected Value 184
7.3 Expectation as an Integral* 192
7.4 Properties of Expectation 199
7.5 Moments 207
7.6 Variance 215
7.7 Conditional Expectation 227
7.8 Inequalities 231
8 Selected Families of Distributions 237
8.1 Bernoulli Trials and Related Distributions 237
8.2 Hypergeometric Distribution 251
8.3 Poisson Distribution and Poisson Process 256
8.4 Exponential, Gamma and Related Distributions 269
8.5 Normal Distribution 276
8.6 Beta Distribution 286
9 Random Samples 293
9.1 Statistics and Sampling Distributions 293
9.2 Distributions Related to Normal 295
9.3 Order Statistics 300
9.4 Generating Random Samples 307
9.5 Convergence 312
9.6 Central Limit Theorem 322
10 Introduction to Statistical Inference 331
10.1 Overview 331
10.2 Basic Models 334
10.3 Sampling 336
10.4 Measurement Scales 342
11 Estimation 347
11.1 Introduction 347
11.2 Consistency 352
11.3 Loss, Risk, and Admissibility 355
11.4 Efficiency 361
11.5 Methods of Obtaining Estimators 368
11.6 Sufficiency 387
11.7 Interval Estimation 403
12 Testing Statistical Hypotheses 419
12.1 Introduction 419
12.2 Intuitive Background 423
12.3 Most Powerful Tests 432
12.4 Uniformly Most Powerful Tests 445
12.5 Unbiased Tests 452
12.6 Generalized Likelihood Ratio Tests 456
12.7 Conditional Tests 463
12.8 Tests and Confidence Intervals 466
12.9 Review of Tests for Normal Distributions 467
12.10 Monte Carlo, Bootstrap, and Permutation Tests 477
14 Linear Models 483
14.1 Introduction 483
14.2 Regression of the First and Second Kind 485
14.3 Distributional Assumptions 491
14.4 Linear Regression in the Normal Case 494
14.5 Testing Linearity 500
14.6 Prediction 503
14.7 Inverse Regression 505
14.8 BLUE 508
14.9 Regression Toward the Mean 510
14.10 Analysis of Variance 512
14.11 One-Way Layout 512
14.12 Two-Way Layout 516
14.13 ANOVA Models with Interaction 518
14.14 Further Extensions 522
15 Rank Methods 525
15.1 Introduction 525
15.2 Glivenko-Cantelli Theorem 526
15.3 Kolmogorov-Smirnov Tests 530
15.4 One-Sample Rank Tests 537
15.5 Two-Sample Rank Tests 544
15.6 Kruskal-Wallis Test 548
16 Analysis of Categorical Data 551
16.1 Introduction 551
16.2 Chi-Square Tests 553
16.3 Homogeneity and Independence 559
16.4 Consistency and Power 565
16.5 2x2 Contingency Tables 570
16.6 r x c Contingency Tables 578
17 Basics of Bayesian Statistics 583
17.1 Introduction 583
17.2 Prior and Posterior Distributions 584
17.3 Bayesian Inference 592
17.4 Final Comments 608
Appendix 1 609
Appendix 2 616
Bibliography 619
Answers to Odd-Numbered Problems 624
Index 632
Index 632MAGDALENA NIEWIADOMSKA-BUGAJ, PHD, is Professor and Chair of the Statistics Department at Western Michigan University. Dr. Niewiadomska-Bugaj's areas of interest include general statistical methodology, nonparametric statistics, classification, and categorical data analysis. She has published over 50 papers, books, and book chapters in theoretical and applied statistics
The late ROBERT BARTOSZYNSKI, PHD, was Professor in the Department of Statistics at The Ohio State University. His scientific contributions included research in the theory of stochastic processes and modeling biological phenomena. Throughout his career, Dr Bartoszynski published books, book chapters, and over 100 journal articles.
