Mathematical Statistics and Data Analysis

1. PROBABILITY. Introduction. Sample Spaces. Probability Measures. Computing Probabilities: Counting Methods. Conditional Probability. Independence. Concluding Remarks. Problems. 2. RANDOM VARIABLES. Discrete Random Variables. Continuous Random Variables. Functions of a Random Variable. Concluding Remarks. Problems. 3. JOINT DISTRIBUTIONS. Introduction. Discrete Random Variables. Continuous Random Variables. Independent Random Variables. Conditional Distributions. Functions of Jointly Distributed Random Variables. Extrema and Order Statistics. Problems. 4. EXPECTED VALUES. The Expected Value of a Random Variable. Variance and Standard Deviation. Covariance and Correlation. Conditional Expectation and Prediction. The Moment-Generating Function. Approximate Methods. Problems. 5. LIMIT THEOREMS. Introduction. The Law of Large Numbers. Convergence in Distribution and the Central Limit Theorem. Problems . 6. DISTRIBUTIONS DERIVED FROM THE NORMAL DISTRIBUTION. Introduction. Chi-Squared, t, and F Distributions. The Sample Mean and Sample Variance. Problems. 7. SURVEY SAMPLING. Introduction. Population Parameters. Simple Random Sampling. Estimation of a Ratio. Stratified Random Sampling. Concluding Remarks. Problems. 8. ESTIMATION OF PARAMETERS AND FITTING OF PROBABILITY DISTRIBUTIONS. Introduction. Fitting the Poisson Distribution to the Emissions of Alpha Particles. Parameter Estimation. The Method of Moments. The Method of Maximum Likelihood. The Bayesian Approach to Parameter Estimation. Efficiency and the Cramer-Rao Lower Bound. Sufficiency. Concluding Remarks. Problems. 9. TESTING HYPOTHESES AND ASSESSING GOODNESS OF FIT. Introduction. The Neyman-Pearson Paradigm. The Duality of Confidence Intervals and Hypothesis Tests. Generalized Likelihood Ratio Tests. Likelihood Ratio Tests for the Multinomial Distribution. The Poisson Dispersion Test. Hanging Rootograms. Probability Plots. Tests for Normality. Concluding Remarks. Problems. 10. SUMMARIZING DATA. Introduction. Methods Based on the Cumulative Distribution Function. Histograms, Density Curves, and Stem-and-Leaf Plots. Measures of Location. Measures of Dispersion. Boxplots. Exploring Relationships with Scatterplots. Concluding Remarks. Problems. 11. COMPARING TWO SAMPLES. Introduction. Comparing Two Independent Samples. Comparing Paired Samples. Experimental Design. Concluding Remarks. Problems. 12. THE ANALYSIS OF VARIANCE. Introduction. The One-Way Layout. The Two-Way Layout. Concluding Remarks. Problems. 13. THE ANALYSIS OF CATEGORICAL DATA. Introduction. Fisher's Exact Test. The Chi-Square Test of Homogeneity. The Chi-Square Test of Independence. Matched-Pairs Designs. Odds Ratios. Concluding Remarks. Problems. 14. LINEAR LEAST SQUARES. Introduction. Simple Linear Regression. The Matrix Approach to Linear Least Squares. Statistical Properties of Least Squares Estimates. Multiple Linear Regression--An Example. Conditional Inference, Unconditional Inference, and the Bootstrap. Concluding Remarks. Problems. 15. DECISION THEORY AND BAYESIAN INFERENCE. Introduction. Decision Theory. The Subjectivist Point of View. Concluding Remarks. Problems. Appendix A. Common Distributions. Appendix B. Tables. Bibliography. Answers to Selected Problems. Author Index. Index to Data Sets. Subject Index.