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.
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