Book:Morris H. DeGroot/Probability and Statistics/Fourth Edition

Subject Matter

 * Statistics

Contents

 * Preface


 * 1 Introduction to Probability
 * 1.1 The History of Probability
 * 1.2 Interpretations of Probability
 * 1.3 Experiments and Events
 * 1.4 Set Theory
 * 1.5 The Definition of Probability
 * 1.6 Finite Sample Spaces
 * 1.7 Counting Methods
 * 1.8 Combinatorial Methods
 * 1.9 Multinomial Coefficients
 * 1.10 The Probability of a Union of Events
 * 1.11 Statistical Swindles
 * 1.12 Supplementary Exercises


 * 2 Conditional Probability
 * 2.1 The Definition of Conditional Probability
 * 2.2 Independent Events
 * 2.3 Bayes' Theorem
 * 2.4 The Gambler's Ruin Problem
 * 2.5 Supplementary Exercises


 * 3 Random Variables and Distributions
 * 3.1 Random Variables and Discrete Distributions
 * 3.2 Continuous Distributions
 * 3.3 The Cumulative Distribution Function
 * 3.4 Bivariate Distributions
 * 3.5 Marginal Distributions
 * 3.6 Conditional Distributions
 * 3.7 Multivariate Distributions
 * 3.8 Functions of a Random Variable
 * 3.9 Functions of Two or More Random Variables
 * 3.10 Markov Chains
 * 3.11 Supplementary Exercises


 * 4 Expectation
 * 4.1 The Expectation of a Random Variable
 * 4.2 Properties of Expectations
 * 4.3 Variance
 * 4.4 Moments
 * 4.5 The Mean and the Median
 * 4.6 Covariance and Correlation
 * 4.7 Conditional Expectation
 * 4.8 Utility
 * 4.9 Supplementary Exercises


 * 5 Special Distributions
 * 5.1 Introduction
 * 5.2 The Bernoulli and Binomial Distributions
 * 5.3 The Hypergeometric Distributions
 * 5.4 The Poisson Distributions
 * 5.5 The Negative Binomial Distributions
 * 5.6 The Normal Distributions
 * 5.7 The Gamma Distributions
 * 5.8 The Beta Distributions
 * 5.9 The Multinomial Distributions
 * 5.10 The Bivariate Normal Distributions
 * 5.11 Supplementary Exercises


 * 6 Large Random Samples
 * 6.1 Introduction
 * 6.2 The Law of Large Numbers
 * 6.3 The Central Limit Theorem
 * 6.4 The Correction for Continuity
 * 6.5 Supplementary Exercises


 * 7 Estimation
 * 7.1 Statistical Inference
 * 7.2 Prior and Posterior Distributions
 * 7.3 Conjugate Prior Distributions
 * 7.4 Bayes Estimators
 * 7.5 Maximum Likelihood Estimators
 * 7.6 Properties of Maximum Likelihood Estimators
 * 7.7 Sufficient Statistics
 * 7.8 Jointly Sufficient Statistics
 * 7.9 Improving an Estimator
 * 7.10 Supplementary Exercises


 * 8 Sampling Distributions of Estimators
 * 8.1 The Sampling Distribution of a Statistic
 * 8.2 The Chi-Square Distributions
 * 8.3 Joint Distribution of the Sample Mean and Sample Variance
 * 8.4 The $t$ Distributions
 * 8.5 Confidence Intervals
 * 8.6 Bayesian Analysis of Samples from a Normal Distribution
 * 8.7 Unbiased Estimators
 * 8.8 Fisher Information
 * 8.9 Supplementary Exercises


 * 9 Testing Hypotheses
 * 9.1 Problems of Testing Hypotheses
 * 9.2 Testing Simple Hypotheses
 * 9.3 Uniformly Most Powerful Tests
 * 9.4 Two-Sided Alternatives
 * 9.5 The $t$ Test
 * 9.6 Comparing the Means of Two Normal Distributions
 * 9.7 The $F$ Distributions
 * 9.8 Bayes Test Procedures
 * 9.9 Foundational Issues
 * 9.10 Supplementary Exercises


 * 10 Categorical Data and Nonparametric Methods
 * 10.1 Tests of Goodness-of-Fit
 * 10.2 Goodness-of-Fit for Composite Hypotheses
 * 10.3 Contingency Tables
 * 10.4 Tests of Homogeneity
 * 10.5 Simpson’s Paradox
 * 10.6 Kolmogorov-Smirnov Tests
 * 10.7 Robust Estimation
 * 10.8 Sign and Rank Tests
 * 10.9 Supplementary Exercises


 * 11 Linear Statistical Models
 * 11.1 The Method of Least Squares
 * 11.2 Regression
 * 11.3 Statistical Inference in Simple Linear Regression
 * 11.4 Bayesian Inference in Simple Linear Regression
 * 11.5 The General Linear Model and Multiple Regression
 * 11.6 Analysis of Variance
 * 11.7 The Two-Way Layout
 * 11.8 The Two-Way Layout with Replications
 * 11.9 Supplementary Exercises


 * 12 Simulation
 * 12.1 What Is Simulation?
 * 12.2 Why Is Simulation Useful?
 * 12.3 Simulating Specific Distributions
 * 12.4 Importance Sampling
 * 12.5 Markov Chain Monte Carlo
 * 12.6 The Bootstrap
 * 12.7 Supplementary Exercises


 * Tables


 * Answers to Odd-Numbered Exercises


 * References


 * Index