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Preface | |
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Discrete Probability Models | |
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Introduction | |
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Sample Spaces, Events, and Probability Measures | |
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Conditional Probability and Independence | |
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Random Variables | |
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Expectation | |
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The Variance | |
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Covariance and Correlation | |
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Special Discrete Distributions | |
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Introduction | |
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The Binomial Distribution | |
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The Hypergeometric Distribution | |
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The Geometric and Negative Binomial Distributions | |
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The Poisson Distribution | |
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Continuous Random Variables | |
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Introduction | |
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Continuous Random Variables | |
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Expected Values and Variances for Continuous Random Variables | |
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Transformations of Random Variables | |
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Joint Densities | |
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Distributions of Functions of Continuous Random Variables | |
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Special Continuous Distributions | |
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Introduction | |
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The Normal Distribution | |
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The Gamma Distribution | |
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Conditional Distributions | |
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Introduction | |
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Conditional Expectations for Discrete Random Variables | |
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Conditional Densities and Expectations for Continuous Random Variables | |
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Moment Generating Functions and Limit Theory | |
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Introduction | |
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Moment Generating Functions | |
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Convergence in Probability and in Distribution and the Weak Law of Large Numbers | |
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The Central Limit Theorem | |
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Estimation | |
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Introduction | |
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Point Estimation | |
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The Method of Moments | |
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Maximum Likelihood | |
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Consistency | |
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The [delta]-Method | |
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Confidence Intervals | |
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Fisher Information, Cramer-Rao Bound and Asymptotic Normality of MLEs | |
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Sufficiency | |
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Testing of Hypotheses | |
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Introduction | |
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The Neyman-Pearson Lemma | |
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The Likelihood Ratio Test | |
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The p-Value and the Relationship between Tests of Hypotheses and Confidence Intervals | |
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The Multivariate Normal, Chi-Square, t, and F Distributions | |
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Introduction | |
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The Multivariate Normal Distribution | |
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The Central and Noncentral Chi-Square Distributions | |
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Student's t-Distribution | |
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The F-Distribution | |
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Nonparametric Statistics | |
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Introduction | |
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The Wilcoxon Test and Estimator | |
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One-Sample Methods | |
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The Kolmogorov-Smirnov Tests | |
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Linear Statistical Models | |
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Introduction | |
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The Principle of Least Squares | |
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Linear Models | |
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F-Tests for H[subscript 0]: [theta] = [Beta subscript 1] X[subscript 1] + ... + [Beta subscript k] X[subscript k][Epsilon] V[subscript 0], a Subspace of V | |
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Two-Way Analysis of Variance | |
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Frequency Data | |
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Introduction | |
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Confidence Intervals on Binomial and Poisson Parameters | |
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Logistic Regression | |
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Two-Way Frequency Tables | |
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Chi-Square Goodness-of-Fit Tests | |
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Miscellaneous Topics | |
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Introduction | |
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Survival Analysis | |
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Bootstrapping | |
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Bayesian Statistics | |
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Sampling | |
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References | |
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Appendix | |
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Answers to Selected Problems | |
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Index | |