An Introduction to Probability and Statistics, 2nd EditionISBN: 9780471348467
744 pages
October 2000

Description
Table of Contents
Preface to the Second Edition xi
Preface to the First Edition xiii
1. Probability 1
1.1 Introduction 1
1.2 Sample Space 2
1.3 Probability Axioms 7
1.4 Combinatorics: Probability on Finite Sample Spaces 21
1.5 Conditional Probability and Bayes Theorem 28
1.6 Independence of Events 33
2. Random Variables and Their Probability Distributions 40
2.1 Introduction 40
2.2 Random Variables 40
2.3 Probability Distribution of a Random Variable 43
2.4 Discrete and Continuous Random Variables 48
2.5 Functions of a Random Variable 57
3. Moments and Generating Functions 69
3.1 Introduction 69
3.2 Moments of a Distribution Function 69
3.3 Generating Functions 85
3.4 Some Moment Inequalities 95
4. Multiple Random Variables 102
4.1 Introduction 102
4.2 Multiple Random Variables 102
4.3 Independent Random Variables 119
4.4 Functions of Several Random Variables 127
4.5 Covariance Correlation and Moments 149
4.6 Conditional Expectation 164
4.7 Order Statistics and Their Distributions 171
5. Some Special Distributions 180
5.1 Introduction 180
5.2 Some Discrete Distributions 180
5.3 Some Continuous Distributions 204
5.4 Bivariate and Multivariate Normal Distributions 238
5.5 Exponential Family of Distributions 251
6. Limit Theorems 256
6.1 Introduction 256
6.2 Modes of Convergence 256
6.3 Weak Law of Large Numbers 274
6.4 Strong Law of Large Numbers 281
6.5 Limiting Moment Generating Functions 289
6.6 Central Limit Theorem 293
7. Sample Moments and Their Distributions 306
7.1 Introduction 306
7.2 Random Sampling 307
7.3 Sample Characteristics and Their Distributions 310
7.4 ChiSquare f and FDistributions: Exact Sampling Distributions 324
7.5 LargeSample Theory 334
7.6 Distribution of (X S2) in Sampling from a Normal Population 339
7.7 Sampling from a Bivariate Normal Distribution 344
8. Parametric Point Estimation 353
8.1 Introduction 353
8.2 Problem of Point Estimation 354
8.3 Sufficiency Completeness and Ancillarity 358
8.4 Unbiased Estimation 377
8.5 Unbiased Estimation (Continued): Lower Bound for the Variance of an Estimator 391
8.6 Substitution Principle (Method of Moments) 406
8.7 Maximum Likelihood Estimators 409
8.8 Bayes and Minimax Estimation 424
8.9 Principle of Equivariance 442
9. NeymanPearson Theory of Testing of Hypotheses 454
9.1 Introduction 454
9.2 Some Fundamental Notions of Hypotheses Testing 454
9.3 NeymanPearson Lemma 464
9.4 Families with Monotone Likelihood Ratio 472
9.5 Unbiased and Invariant Tests 479
9.6 Locally Most Powerful Tests 486
10. Some Further Results of Hypothesis Testing 490
10.1 Introduction 490
10.2 Generalized Likelihood Ratio Tests 490
10.3 ChiSquare Tests 500
10.4 /Tests 512
10.5 FTests 518
10.6 Bayes and Minimax Procedures 520
11. Confidence Estimation 527
11.1 Introduction 527
11.2 Some Fundamental Notions of Confidence Estimation 527
11.3 Methods of Finding Confidence Intervals 532
11.4 ShortestLength Confidence Intervals 546
11.5 Unbiased and Equivariant Confidence Intervals 553
12. General Linear Hypothesis 561
12.1 Introduction 561
12.2 General Linear Hypothesis 561
12.3 Regression Model 569
12.4 OneWay Analysis of Variance 577
12.5 TwoWay Analysis of Variance with One Observation per Cell 583
12.6 TwoWay Analysis of Variance with Interaction 590
13. Nonparametric Statistical Inference 598
13.1 Introduction 598
13.2 UStatistics 598
13.3 Some SingleSample Problems 608
13.4 Some TwoSample Problems 624
13.5 Tests of Independence 633
13.6 Some Applications of Order Statistics 644
13.7 Robustness 650
References 663
Frequently Used Symbols and Abbreviations 669
Statistical Tables 673
Answers to Selected Problems 693
Author Index 705
Subject Index 707
Reviews
"this book is fascinating" (Short Book Reviews  Publication of the Int. Statistical Institute, December 2001)
"This text is for mathematics specialists..." (Short Book Reviews, Vol. 21, No. 3, December 2001)