O'Reilly logo

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

An Introduction to Probability and Statistics, 3rd Edition

Book Description

A well-balanced introduction to probability theory and mathematical statistics

Featuring updated material, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided intothree parts, the Third Edition begins by presenting the fundamentals and foundationsof probability. The second part addresses statistical inference, and the remainingchapters focus on special topics.

An Introduction to Probability and Statistics, Third Edition includes:

  • A new section on regression analysis to include multiple regression, logistic regression, and Poisson regression

  • A reorganized chapter on large sample theory to emphasize the growing role of asymptotic statistics

  • Additional topical coverage on bootstrapping, estimation procedures, and resampling

  • Discussions on invariance, ancillary statistics, conjugate prior distributions, and invariant confidence intervals

  • Over 550 problems and answers to most problems, as well as 350 worked out examples and 200 remarks

  • Numerous figures to further illustrate examples and proofs throughout

  • An Introduction to Probability and Statistics, Third Edition is an ideal reference and resource for scientists and engineers in the fields of statistics, mathematics, physics, industrial management, and engineering. The book is also an excellent text for upper-undergraduate and graduate-level students majoring in probability and statistics.

    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