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Preface | |
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Basics of Probability | |
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Introduction | |
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Basic Concepts and Definitions | |
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Counting Problems | |
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Axioms of Probability and the Addition Rule | |
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Conditional Probability and the Multiplication Rule | |
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Bayes' Theorem | |
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Independent Events | |
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Discrete Random Variables | |
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Introduction | |
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Probability Mass Functions | |
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The Hypergeometric and Binomial Distributions | |
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The Poisson Distribution | |
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Mean and Variance | |
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Functions of a Random Variable | |
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The Moment-Generating Function | |
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Continuous Random Variables | |
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Introduction | |
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Definitions | |
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The Uniform and Exponential Distributions | |
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The Normal Distribution | |
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Functions of Continuous Random Variables | |
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Joint Distributions | |
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Functions of Independent Random Variables | |
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The Central Limit Theorem | |
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The Gamma and Related Distributions | |
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Approximating the Binomial Distribution | |
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Statistics | |
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What Is Statistics? | |
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Summarizing Data | |
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Maximum Likelihood Estimates | |
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Sampling Distributions | |
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Confidence Intervals for a Proportion | |
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Confidence Intervals for a Mean | |
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Confidence Intervals for a Variance | |
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Confidence Intervals for Differences | |
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Sample Size | |
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Assessing Normality | |
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Hypothesis Testing | |
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Introduction | |
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Testing Claims About a Proportion | |
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Testing Claims About a Mean | |
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Comparing Two Proportions | |
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Comparing Two Variances | |
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Comparing Two Means | |
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Goodness-of-Fit Tests | |
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Test of Independence | |
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One-Way ANOVA | |
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Two-Way ANOVA | |
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Simple Regression | |
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Introduction | |
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Covariance and Correlation | |
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Method of Least Squares | |
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The Simple Linear Model | |
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Sums of Squares and ANOVA | |
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Nonlinear Regression | |
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Multiple Regression | |
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Nonparametric Statistics | |
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Introduction | |
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The Sign Test | |
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The Wilcoxon Signed-Rank Test | |
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The Wilcoxon Rank-Sum Test | |
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The Runs Test for Randomness | |
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Proofs of Selected Theorems | |
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A Proof of Theorem 3.7.5 | |
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A Proof of the Central Limit Theorem | |
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A Proof of the Limit Theorem of De Moivre and Laplace | |
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A Proof of Theorem 4.6.1 | |
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Confidence Intervals for the Difference of Two Means | |
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Coefficients in the Linear Regression Equation | |
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Wilcoxon Signed-Rank Test Distribution | |
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Software Basics | |
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Minitab | |
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R | |
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Excel | |
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TI-83/84 Calculators | |
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Tables | |
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Answers to Selected Exercises | |
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Index | |