Title Page
Contents
Preface
1. Probability
1.1 Introduction
1.2 Sample Spaces
1.3 Probability Measures
1.4 Computing Probabilities: Counting Methods
1.5 Conditional Probability
1.6 Independence
1.7 Concluding Remarks
1.8 Problems
2. Random Variables
2.1 Discrete Random Variables
2.2 Continuous Random Variables
2.3 Functions of a Random Variable
2.4 Concluding Remarks
2.5 Problems
3. Joint Distributions
3.1 Introduction
3.2 Discrete Random Variables
3.3 Continuous Random Variables
3.4 Independent Random Variables
3.5 Conditional Distributions
3.6 Functions of Jointly Distributed Random Variables
3.7 Extrema and Order Statistics
3.8 Problems
4. Expected Values
4.1 The Expected Value of a Random Variable
4.2 Variance and Standard Deviation
4.3 Covariance and Correlation
4.4 Conditional Expectation and Prediction
4.5 The Moment-Generating Function
4.6 Approximate Methods
4.7 Problems
5. Limit Theorems
5.1 Introduction
5.2 The Law of Large Numbers
5.3 Convergence in Distribution and the Central Limit Theorem
5.4 Problems
6. Distributions Derived from the Normal Distribution
6.1 Introduction
6.2 Ο[sup(2)], t, and F Distributions
6.3 The Sample Mean and the Sample Variance
6.4 Problems
7. Survey Sampling
7.1 Introduction
7.2 Population Parameters
7.3 Simple Random Sampling
7.4 Estimation of a Ratio
7.5 Stratified Random Sampling
7.6 Concluding Remarks
7.7 Problems
8. Estimation of Parameters and Fitting of Probability Distributions
8.1 Introduction
8.2 Fitting the Poisson Distribution to Emissions of Alpha Particles
8.3 Parameter Estimation
8.4 The Method of Moments
8.5 The Method of Maximum Likelihood
8.6 The Bayesian Approach to Parameter Estimation
8.7 Efficiency and the CramΓ©r-Rao Lower Bound
8.8 Sufficieny
8.9 Concluding Remarks
8.10 Problems
9. Testing Hypotheses and Assessing Goodness of Fit
9.1 Introduction
9.2 The Neyman-Pearson Paradigm
9.3 The Duality of Confidence Intervals and Hypothesis Tests
9.4 Generalized Likelihood Ratio Tests
9.5 Likelihood Ratio Tests for the Multinomial Distribution
9.6 The Poisson Dispersion Test
9.7 Hanging Rootograms
9.8 Probability Plots
9.9 Tests for Normality
9.10 Concluding Remarks
9.11 Problems
10. Summarizing Data
10.1 Introduction
10.2 Methods Based on the Cumulative Distribution Function
10.3 Histograms, Density Curves, and Stem-and-Leaf Plots
10.4 Measures of Location
10.5 Measures of Dispersion
10.6 Boxplots
10.7 Exploring Relationships with Scatterplots
10.8 Concluding Remarks
10.9 Problems
11. Comparing Two Samples
11.1 Introduction
11.2 Comparing Two Independent Samples
11.3 Comparing Paired Samples
11.4 Experimental Design
11.5 Concluding Remarks
11.6 Problems
12. The Analysis of Variance
12.1 Introduction
12.2 The One-Way Layout
12.3 The Two-Way Layout
12.4 Concluding Remarks
12.5 Problems
13. The Analysis of Categorical Data
13.1 Introduction
13.2 Fisher's Exact Test
13.3 The Chi-Square Test of Homogeneity
13.4 The Chi-Square Test of Independence
13.5 Matched-Pairs Designs
13.6 Odds Ratios
13.7 Concluding Remarks
13.8 Problems
14. Linear Least Squares
14.1 Introduction
14.2 Simple Linear Regression
14.3 The Matrix Approach to Linear Least Squares
14.4 Statistical Properties of Least Squares Estimates
14.5 Multiple Linear RegressionβAn Example
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap
14.7 Local Linear Smoothing
14.8 Concluding Remarks
14.9 Problems
APPENDIX A: Common Distributions
APPENDIX B: Tables
Bibliography
Answers to Selected Problems
Author Index
Applications Index
Subject Index
Credits
Errata