An Introduction to Probability and Statistics, 3rd Edition

Table of contents

1. COVER
2. TITLE PAGE
3. PREFACE TO THE THIRD EDITION
4. PREFACE TO THE SECOND EDITION
5. PREFACE TO THE FIRST EDITION
6. ACKNOWLEDGMENTS
7. ENUMERATION OF THEOREMS AND REFERENCES
8. 1 PROBABILITY
   1. 1.1 INTRODUCTION
   2. 1.2 SAMPLE SPACE
   3. 1.3 PROBABILITY AXIOMS
   4. 1.4 COMBINATORICS: PROBABILITY ON FINITE SAMPLE SPACES
   5. 1.5 CONDITIONAL PROBABILITY AND BAYES THEOREM
   6. 1.6 INDEPENDENCE OF EVENTS
9. 2 RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS
   1. 2.1 INTRODUCTION
   2. 2.2 RANDOM VARIABLES
   3. 2.3 PROBABILITY DISTRIBUTION OF A RANDOM VARIABLE
   4. 2.4 DISCRETE AND CONTINUOUS RANDOM VARIABLES
   5. 2.5 FUNCTIONS OF A RANDOM VARIABLE
10. 3 MOMENTS AND GENERATING FUNCTIONS
    1. 3.1 INTRODUCTION
    2. 3.2 MOMENTS OF A DISTRIBUTION FUNCTION
    3. 3.3 GENERATING FUNCTIONS
    4. 3.4 SOME MOMENT INEQUALITIES
11. 4 MULTIPLE RANDOM VARIABLES
    1. 4.1 INTRODUCTION
    2. 4.2 MULTIPLE RANDOM VARIABLES
    3. 4.3 INDEPENDENT RANDOM VARIABLES
    4. 4.4 FUNCTIONS OF SEVERAL RANDOM VARIABLES
    5. 4.5 COVARIANCE, CORRELATION AND MOMENTS
    6. 4.6 CONDITIONAL EXPECTATION
    7. 4.7 ORDER STATISTICS AND THEIR DISTRIBUTIONS
12. 5 SOME SPECIAL DISTRIBUTIONS
    1. 5.1 INTRODUCTION
    2. 5.2 SOME DISCRETE DISTRIBUTIONS
    3. 5.3 SOME CONTINUOUS DISTRIBUTIONS
    4. 5.4 BIVARIATE AND MULTIVARIATE NORMAL DISTRIBUTIONS
    5. 5.5 EXPONENTIAL FAMILY OF DISTRIBUTIONS
13. 6 SAMPLE STATISTICS AND THEIR DISTRIBUTIONS
    1. 6.1 INTRODUCTION
    2. 6.2 RANDOM SAMPLING
    3. 6.3 SAMPLE CHARACTERISTICS AND THEIR DISTRIBUTIONS
    4. 6.4 CHI-SQUARE, t-, AND F-DISTRIBUTIONS: EXACT SAMPLING DISTRIBUTIONS
    5. 6.5 DISTRIBUTION OF IN SAMPLING FROM A NORMAL POPULATION
    6. 6.6 SAMPLING FROM A BIVARIATE NORMAL DISTRIBUTION
14. 7 BASIC ASYMPTOTICS: LARGE SAMPLE THEORY
    1. 7.1 INTRODUCTION
    2. 7.2 MODES OF CONVERGENCE
    3. 7.3 WEAK LAW OF LARGE NUMBERS
    4. 7.4 STRONG LAW OF LARGE NUMBERS†
    5. 7.5 LIMITING MOMENT GENERATING FUNCTIONS
    6. 7.6 CENTRAL LIMIT THEOREM
    7. 7.7 LARGE SAMPLE THEORY
15. 8 PARAMETRIC POINT ESTIMATION
    1. 8.1 INTRODUCTION
    2. 8.2 PROBLEM OF POINT ESTIMATION
    3. 8.3 SUFFICIENCY, COMPLETENESS AND ANCILLARITY
    4. 8.4 UNBIASED ESTIMATION
    5. 8.5 UNBIASED ESTIMATION (CONTINUED): A LOWER BOUND FOR THE VARIANCE OF AN ESTIMATOR
    6. 8.6 SUBSTITUTION PRINCIPLE (METHOD OF MOMENTS)
    7. 8.7 MAXIMUM LIKELIHOOD ESTIMATORS
    8. 8.8 BAYES AND MINIMAX ESTIMATION
    9. 8.9 PRINCIPLE OF EQUIVARIANCE
16. 9 NEYMAN–PEARSON THEORY OF TESTING OF HYPOTHESES
    1. 9.1 INTRODUCTION
    2. 9.2 SOME FUNDAMENTAL NOTIONS OF HYPOTHESES TESTING
    3. 9.3 NEYMAN–PEARSON LEMMA
    4. 9.4 FAMILIES WITH MONOTONE LIKELIHOOD RATIO
    5. 9.5 UNBIASED AND INVARIANT TESTS
    6. 9.6 LOCALLY MOST POWERFUL TESTS
17. 10 SOME FURTHER RESULTS ON HYPOTHESES TESTING
    1. 10.1 INTRODUCTION
    2. 10.2 GENERALIZED LIKELIHOOD RATIO TESTS
    3. 10.3 CHI-SQUARE TESTS
    4. 10.4 t-TESTS
    5. 10.5 F-TESTS
    6. 10.6 BAYES AND MINIMAX PROCEDURES
18. 11 CONFIDENCE ESTIMATION
    1. 11.1 INTRODUCTION
    2. 11.2 SOME FUNDAMENTAL NOTIONS OF CONFIDENCE ESTIMATION
    3. 11.3 METHODS OF FINDING CONFIDENCE INTERVALS
    4. 11.4 SHORTEST-LENGTH CONFIDENCE INTERVALS
    5. 11.5 UNBIASED AND EQUIVARIANT CONFIDENCE INTERVALS
    6. 11.6 RESAMPLING: BOOTSTRAP METHOD
19. 12 GENERAL LINEAR HYPOTHESIS
    1. 12.1 INTRODUCTION
    2. 12.2 GENERAL LINEAR HYPOTHESIS
    3. 12.3 REGRESSION ANALYSIS
    4. 12.4 ONE-WAY ANALYSIS OF VARIANCE
    5. 12.5 TWO-WAY ANALYSIS OF VARIANCE WITH ONE OBSERVATION PER CELL
    6. 12.6 TWO-WAY ANALYSIS OF VARIANCE WITH INTERACTION
20. 13 NONPARAMETRIC STATISTICAL INFERENCE
    1. 13.1 INTRODUCTION
    2. 13.2 U-STATISTICS
    3. 13.3 SOME SINGLE-SAMPLE PROBLEMS
    4. 13.4 SOME TWO-SAMPLE PROBLEMS
    5. 13.5 TESTS OF INDEPENDENCE
    6. 13.6 SOME APPLICATIONS OF ORDER STATISTICS
    7. 13.7 ROBUSTNESS
21. FREQUENTLY USED SYMBOLS AND ABBREVIATIONS
22. REFERENCES
23. STATISTICAL TABLES
24. ANSWERS TO SELECTED PROBLEMS
25. AUTHOR INDEX
26. SUBJECT INDEX
27. WILEY SERIES IN PROBABILITY AND STATISTICS
28. END USER LICENSE AGREEMENT