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Probability, Statistics, and Stochastic Processes, 2nd Edition

Book Description

Praise for the First Edition

". . . an excellent textbook . . . well organized and neatly written."

Mathematical Reviews

". . . amazingly interesting . . ."

Technometrics

Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields.

Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including:

  • Consistency of point estimators

  • Large sample theory

  • Bootstrap simulation

  • Multiple hypothesis testing

  • Fisher's exact test and Kolmogorov-Smirnov test

  • Martingales, renewal processes, and Brownian motion

  • One-way analysis of variance and the general linear model

Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Preface to the First Edition
  6. The Book
  7. The People
  8. Chapter 1: Basic Probability Theory
    1. 1.1 Introduction
    2. 1.2 Sample Spaces and Events
    3. 1.3 The Axioms of Probability
    4. 1.4 Finite Sample Spaces and Combinatorics
    5. 1.5 Conditional Probability and Independence
    6. 1.6 The Law of Total Probability and Bayes' Formula
    7. Problems
  9. Chapter 2: Random Variables
    1. 2.1 Introduction
    2. 2.2 Discrete Random Variables
    3. 2.3 Continuous Random Variables
    4. 2.4 Expected Value and Variance
    5. 2.5 Special Discrete Distributions
    6. 2.6 The Exponential Distribution
    7. 2.7 The Normal Distribution
    8. 2.8 Other Distributions
    9. 2.9 Location Parameters
    10. 2.10 The Failure Rate Function
    11. Problems
  10. Chapter 3: Joint Distributions
    1. 3.1 Introduction
    2. 3.2 The Joint Distribution Function
    3. 3.3 Discrete Random Vectors
    4. 3.4 Jointly Continuous Random Vectors
    5. 3.5 Conditional Distributions and Independence
    6. 3.6 Functions of Random Vectors
    7. 3.7 Conditional Expectation
    8. 3.8 Covariance and Correlation
    9. 3.9 The Bivariate Normal Distribution
    10. 3.10 Multidimensional Random Vectors
    11. 3.11 Generating Functions
    12. 3.12 The Poisson Process
    13. Problems
  11. Chapter 4: Limit Theorems
    1. 4.1 Introduction
    2. 4.2 The Law of Large Numbers
    3. 4.3 The Central Limit Theorem
    4. 4.4 Convergence in Distribution
    5. Problems
  12. Chapter 5: Simulation
    1. 5.1 Introduction
    2. 5.2 Random Number Generation
    3. 5.3 Simulation of Discrete Distributions
    4. 5.4 Simulation of Continuous Distributions
    5. 5.5 Miscellaneous
    6. Problems
  13. Chapter 6: Statistical Inference
    1. 6.1 Introduction
    2. 6.2 Point Estimators
    3. 6.3 Confidence Intervals
    4. 6.4 Estimation Methods
    5. 6.5 Hypothesis Testing
    6. 6.6 Further Topics in Hypothesis Testing
    7. 6.7 Goodness of Fit
    8. 6.8 Bayesian Statistics
    9. 6.9 Nonparametric Methods
    10. Problems
  14. Chapter 7: Linear Models
    1. 7.1 Introduction
    2. 7.2 Sampling Distributions
    3. 7.3 Single Sample Inference
    4. 7.4 Comparing Two Samples
    5. 7.5 Analysis of Variance
    6. 7.6 Linear Regression
    7. 7.7 The General Linear Model
    8. 7.8 Problems
  15. Chapter 8: Stochastic Processes
    1. 8.1 Introduction
    2. 8.2 Discrete -Time Markov Chains
    3. 8.3 Random Walks and Branching Processes
    4. 8.4 Continuous -Time Markov Chains
    5. 8.5 Martingales
    6. 8.6 Renewal Processes
    7. 8.7 Brownian Motion
    8. Problems
  16. Appendix A: Tables
  17. Appendix B: Answers to Selected Problems
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
  18. Further Reading
  19. Index