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Preface | |

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Probability | |

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Introduction | |

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Sample Spaces | |

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Probability Measures | |

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Computing Probabilities: Counting Methods | |

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The Multiplication Principle | |

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Permutations and Combinations | |

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Conditional Probability | |

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Independence | |

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Concluding Remarks | |

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Problems | |

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Random Variables | |

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Discrete Random Variables | |

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Bernoulli Random Variables | |

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The Binomial Distribution | |

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The Geometric and Negative Binomial Distributions | |

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The Hypergeometric Distribution | |

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The Poisson Distribution | |

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Continuous Random Variables | |

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The Exponential Density | |

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The Gamma Density | |

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The Normal Distribution | |

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The Beta Density | |

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Functions of a Random Variable | |

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Concluding Remarks | |

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Problems | |

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Joint Distributions | |

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Introduction | |

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Discrete Random Variables | |

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Continuous Random Variables | |

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Independent Random Variables | |

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Conditional Distributions | |

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The Discrete Case | |

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The Continuous Case | |

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Functions of Jointly Distributed Random Variables | |

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Sums and Quotients | |

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The General Case | |

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Extrema and Order Statistics | |

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Problems | |

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Expected Values | |

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The Expected Value of a Random Variable | |

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Expectations of Functions of Random Variables | |

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Expectations of Linear Combinations of Random Variables | |

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Variance and Standard Deviation | |

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A Model for Measurement Error | |

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Covariance and Correlation | |

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Conditional Expectation and Prediction | |

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Definitions and Examples | |

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Prediction | |

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The Moment-Generating Function | |

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Approximate Methods | |

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Problems | |

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Limit Theorems | |

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Introduction | |

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The Law of Large Numbers | |

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Convergence in Distribution and the Central Limit Theorem | |

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Problems | |

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Distributions Derived from the Normal Distribution | |

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Introduction | |

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x[superscript 2], t, and F Distributions | |

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The Sample Mean and the Sample Variance | |

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Problems | |

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Survey Sampling | |

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Introduction | |

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Population Parameters | |

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Simple Random Sampling | |

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The Expectation and Variance of the Sample Mean | |

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Estimation of the Population Variance | |

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The Normal Approximation to the Sampling Distribution of X | |

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Estimation of a Ratio | |

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Stratified Random Sampling | |

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Introduction and Notation | |

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Properties of Stratified Estimates | |

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Methods of Allocation | |

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Concluding Remarks | |

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Problems | |

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Estimation of Parameters and Fitting of Probability Distributions | |

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Introduction | |

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Fitting the Poisson Distribution to Emissions of Alpha Particles | |

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Parameter Estimation | |

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The Method of Moments | |

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The Method of Maximum Likelihood | |

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Maximum Likelihood Estimates of Multinomial Cell Probabilities | |

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Large Sample Theory for Maximum Likelihood Estimates | |

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Confidence Intervals from Maximum Likelihood Estimates | |

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The Bayesian Approach to Parameter Estimation | |

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Further Remarks on Priors | |

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Large Sample Normal Approximation to the Posterior | |

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Computational Aspects | |

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Efficiency and the Cramer-Rao Lower Bound | |

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An Example: The Negative Binomial Distribution | |

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Sufficiency | |

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A Factorization Theorem | |

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The Rao-Blackwell Theorem | |

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Concluding Remarks | |

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Problems | |

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Testing Hypotheses and Assessing Goodness of Fit | |

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Introduction | |

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The Neyman-Pearson Paradigm | |

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Specification of the Significance Level and the Concept of a p-value | |

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The Null Hypothesis | |

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Uniformly Most Powerful Tests | |

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The Duality of Confidence Intervals and Hypothesis Tests | |

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Generalized Likelihood Ratio Tests | |

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Likelihood Ratio Tests for the Multinomial Distribution | |

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The Poisson Dispersion Test | |

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Hanging Rootograms | |

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Probability Plots | |

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Tests for Normality | |

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Concluding Remarks | |

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Problems | |

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Summarizing Data | |

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Introduction | |

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Methods Based on the Cumulative Distribution Function | |

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The Empirical Cumulative Distribution Function | |

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The Survival Function | |

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Quantile-Quantile Plots | |

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Histograms, Density Curves, and Stem-and-Leaf Plots | |

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Measures of Location | |

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The Arithmetic Mean | |

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The Median | |

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The Trimmed Mean | |

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M Estimates | |

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Comparison of Location Estimates | |

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Estimating Variability of Location Estimates by the Bootstrap | |

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Measures of Dispersion | |

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Boxplots | |

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Exploring Relationships with Scatterplots | |

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Concluding Remarks | |

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Problems | |

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Comparing Two Samples | |

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Introduction | |

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Comparing Two Independent Samples | |

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Methods Based on the Normal Distribution | |

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Power | |

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A Nonparametric Method-The Mann-Whitney Test | |

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Bayesian Approach | |

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Comparing Paired Samples | |

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Methods Based on the Normal Distribution | |

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A Nonparametric Method-The Signed Rank Test | |

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An Example-Measuring Mercury Levels in Fish | |

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Experimental Design | |

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Mammary Artery Ligation | |

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The Placebo Effect | |

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The Lanarkshire Milk Experiment | |

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The Portacaval Shunt | |

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FD&C Red No. 40 | |

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Further Remarks on Randomization | |

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Observational Studies, Confounding, and Bias in Graduate Admissions | |

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Fishing Expeditions | |

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Concluding Remarks | |

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Problems | |

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The Analysis of Variance | |

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Introduction | |

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The One-Way Layout | |

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Normal Theory; the F Test | |

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The Problem of Multiple Comparisons | |

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A Nonparametric Method-The Kruskal-Wallis Test | |

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The Two-Way Layout | |

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Additive Parametrization | |

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Normal Theory for the Two-Way Layout | |

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Randomized Block Designs | |

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A Nonparametric Method-Friedman's Test | |

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Concluding Remarks | |

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Problems | |

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The Analysis of Categorical Data | |

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Introduction | |

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Fisher's Exact Test | |

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The Chi-Square Test of Homogeneity | |

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The Chi-Square Test of Independence | |

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Matched-Pairs Designs | |

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Odds Ratios | |

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Concluding Remarks | |

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Problems | |

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Linear Least Squares | |

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Introduction | |

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Simple Linear Regression | |

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Statistical Properties of the Estimated Slope and Intercept | |

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Assessing the Fit | |

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Correlation and Regression | |

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The Matrix Approach to Linear Least Squares | |

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Statistical Properties of Least Squares Estimates | |

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Vector-Valued Random Variables | |

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Mean and Covariance of Least Squares Estimates | |

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Estimation of [gamma superscript 2] | |

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Residuals and Standardized Residuals | |

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Inference about [beta] | |

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Multiple Linear Regression-An Example | |

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Conditional Inference, Unconditional Inference, and the Bootstrap | |

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Local Linear Smoothing | |

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Concluding Remarks | |

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Problems | |

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Common Distributions | |

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Tables | |

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Bibliography | |

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Answers to Selected Problems | |

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Author Index | |

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Applications Index | |

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Subject Index | |