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PREFACE
CHAPTER 1 Probability and Distributions
  1.1 Introduction
  1.2 Set Theory
  1.3 The Probability Set Function
  1.4 Conditional Probability and Independence
  1.5 Random Variables of the Discrete Type
  1.6 Random Variables of the Continuous Type
  1.7 Properties of the Distribution Function
  1.8 Expectation of a Random Variable
  1.9 Some Special Expectations
  l.10 Chebyshev's Inequality
CHAPTER 2 Multivariate Distributions
  2.1 Distributions of Two Random Variables
  2.2 Conditional Distributions and Expectations
  2.3 The Correlation Coefficient
  2.4 Independent Random Variables
  2.5 Extension to Several Random Variables
CHAPTER 3 Some Special Distributions
  3.1 The Binomial and Related Distributions
  3.2 The Poisson Distribution
  3.3 The Gamma and Chi-Square Distributions
  3.4 The Normal Distribution
  3.5 The Bivariate Normal Distribution
CHAPTER 4 Distributions of Functions of Random Variables
  4.1 Sampling Theory
  4.2 Transformations of Variables of the Discrete Type
  4.3 Transformations of Variables of the Continuous Type
  4.4 The Beta,t,and F Distributions
  4.5 Extensions of the Change-of-Variable Technique
  4.6 Distributions of Order Statistics
  4.7 The Moment-Generating-Function Technique
  4.8 The Distributions of X and nS2/Q2
  4.9 Expectations of Functions of Random Variables
*4.10 The Multivariate Normal Distribution
CHAPTER 5Limiting Distributions
  5.1 Convergence in Distribution
  5.2 Convergence in Probability
  5.3 Limiting Moment-Generating Functions
  5.4 The Central Limit Theorem
  5.5 Some Theorems on Limiting Distributions
CHAPTER 6 Introduction to Statistical Inference
  6.1 Point Estimation
  6.2 Confidence Intervals for Means
  6.3 Confidence Intervals for Differences of Means
  6.4 Tests of Statistical Hypotheses
  6.5 Additional Comments About Statistical Tests
  6.6 Chi-Square Tests
CHAPTER 7Sufficient Statistics
  7.1 Measures of Quality of Estimators
  7.2 A Sufficient Statistic for a Parameter
  7.3 Properties of a Sufficient Statistic
  7.4 Completeness and Uniqueness
  7.5 The Exponential Class of Probability Density Functions
  7.6 Functions of a Parameter
  7.7 The Case of Several Parameters
  7.8 Minimal Sufficient and Ancillary Statistics
  7.9 Sufficiency,Completeness,and Independence
CHAPTER 8 More About Estimation
  8.1 Bayesian Estimation
  8.2 Fisher Information and the Rao-Cramé Inequality
  8.3 Limiting Distributions of Maximum Likelihood Estimators
  8.4 Robust M-Estimation
CHAPTER 9 Theory of Statistical Tests
  9.1 Certain Best Tests
  9.2 Uniformly Most Powerful Tests
  9.3 Likelihood Ratio Tests
  9.4 The Sequential Probability Ratio Test
  9.5 Minimax,Bayesian,and Classification Procedures
CHAPTER 10 Inferences About Normal Models
  10.1 The Distributions of Certain Quadratic Forms
  10.2 A Test of the Equality of Several Means
  10.3 Noncentral X2 and Noncentral F
  10.4 Multiple Comparisons
  10.5 The Analysis of Variance
  10.6 A Regression Problem
  10.7 A Test of Independence
  10.8 The Distributions of Certain Quadratic Forms
  10.9 The Independence of Certain Quadratic Forms
CHAPTER 11 Nonparametric Methods
  11.1 Confidence Intervals for Distribution Quantiles
  11.2 Tolerance Limits for Distributions
  11.3 The Sign Test
  11.4 A Test of Wilcoxon
  11.5 The Equality of Two Distributions
  11.6 The Mann-Whitney-Wilcoxon Test
  11.7 Distributions Under Alternative Hypotheses
  11.8 Linear Rank Statistics
  11.9 Adaptive Nonparametric Methods
APPENDIX A
  References
APPENDIX B
  Tables
APPENDIX C
  Answers to Selected Exercises
INDEX