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Preface | |
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Note to the Student | |
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What Is Statistics? | |
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Introduction | |
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Characterizing a Set of Measurements: Graphical Methods | |
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Characterizing a Set of Measurements: Numerical Methods | |
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How Inferences Are Made | |
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Theory and Reality | |
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Summary | |
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Probability | |
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Introduction | |
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Probability and Inference | |
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A Review of Set Notation | |
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A Probabilistic Model for an Experiment: The Discrete Case | |
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Calculating the Probability of an Event: The Sample-Point Method | |
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Tools for Counting Sample Points | |
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Conditional Probability and the Independence of Events | |
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Two Laws of Probability | |
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Calculating the Probability of an Event: The Event-Composition Method | |
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The Law of Total Probability and Bayes' Rule | |
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Numerical Events and Random Variables | |
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Random Sampling | |
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Summary | |
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Discrete Random Variables and Their Probability Distributions | |
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Basic Definition | |
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The Probability Distribution for a Discrete Random Variable | |
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The Expected Value of a Random Variable or a Function of a Random Variable | |
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The Binomial Probability Distribution | |
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The Geometric Probability Distribution | |
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The Negative Binomial Probability Distribution (Optional) | |
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The Hypergeometric Probability Distribution | |
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The Poisson Probability Distribution | |
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Moments and Moment-Generating Functions | |
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Probability-Generating Functions (Optional) | |
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Tchebysheff's Theorem | |
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Summary | |
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Continuous Random Variables and Their Probability Distributions | |
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Introduction | |
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The Probability Distribution for a Continuous Random Variable | |
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Expected Values for Continuous Random Variables | |
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The Uniform Probability Distribution | |
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The Normal Probability Distribution | |
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The Gamma Probability Distribution | |
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The Beta Probability Distribution | |
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Some General Comments | |
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Other Expected Values | |
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Tchebysheff's Theorem | |
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Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) | |
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Summary | |
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Multivariate Probability Distributions | |
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Introduction | |
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Bivariate and Multivariate Probability Distributions | |
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Marginal and Conditional Probability Distributions | |
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Independent Random Variables | |
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The Expected Value of a Function of Random Variables | |
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Special Theorems | |
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The Covariance of Two Random Variables | |
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The Expected Value and Variance of Linear Functions of Random Variables | |
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The Multinomial Probability Distribution | |
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The Bivariate Normal Distribution (Optional) | |
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Conditional Expectations | |
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Summary | |
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Functions of Random Variables | |
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Introduction | |
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Finding the Probability Distribution of a Function of Random Variables | |
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The Method of Distribution Functions | |
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The Method of Transformations | |
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The Method of Moment-Generating Functions | |
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Multivariable Transformations Using Jacobians (Optional) | |
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Order Statistics | |
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Summary | |
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Sampling Distributions and the Central Limit Theorem | |
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Introduction | |
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Sampling Distributions Related to the Normal Distribution | |
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The Central Limit Theorem | |
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A Proof of the Central Limit Theorem (Optional) | |
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The Normal Approximation to the Binomial Distribution | |
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Summary | |
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Estimation | |
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Introduction | |
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The Bias and Mean Square Error of Point Estimators | |
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Some Common Unbiased Point Estimators | |
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Evaluating the Goodness of a Point Estimator | |
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Confidence Intervals | |
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Large-Sample Confidence Intervals | |
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Selecting the Sample Size | |
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Small-Sample Confidence Intervals for [mu] and [mu subscript 1] - [mu subscript 2] | |
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Confidence Intervals for [sigma superscript 2] | |
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Summary | |
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Properties of Point Estimators and Methods of Estimation | |
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Introduction | |
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Relative Efficiency | |
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Consistency | |
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Sufficiency | |
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The Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimation | |
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The Method of Moments | |
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The Method of Maximum Likelihood | |
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Some Large-Sample Properties of MLEs (Optional) | |
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Summary | |
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Hypothesis Testing | |
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Introduction | |
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Elements of a Statistical Test | |
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Common Large-Sample Tests | |
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Calculating Type II Error Probabilities and Finding the Sample Size for the Z Test | |
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Relationships Between Hypothesis-Testing Procedures and Confidence Intervals | |
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Another Way to Report the Results of a Statistical Test: Attained Significance Levels or p-Values | |
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Some Comments on the Theory of Hypothesis Testing | |
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Small-Sample Hypothesis Testing for [mu] and [mu subscript 1] - [mu subscript 2] | |
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Testing Hypotheses Concerning Variances | |
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Power of Tests and the Neyman-Pearson Lemma | |
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Likelihood Ratio Tests | |
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Summary | |
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Linear Models and Estimation by Least Squares | |
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Introduction | |
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Linear Statistical Models | |
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The Method of Least Squares | |
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Properties of the Least Squares Estimators: Simple Linear Regression | |
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Inferences Concerning the Parameters [beta subscript i] | |
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Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression | |
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Predicting a Particular Value of Y Using Simple Linear Regression | |
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Correlation | |
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Some Practical Examples | |
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Fitting the Linear Model by Using Matrices | |
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Linear Functions of the Model Parameters: Multiple Linear Regression | |
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Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression | |
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Predicting a Particular Value of Y Using Multiple Regression | |
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A Test for H[subscript 0]: [beta subscript g+1] = [beta subscript g+2] = ... = [beta subscript k] = 0 | |
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Summary and Concluding Remarks | |
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Considerations in Designing Experiments | |
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The Elements Affecting the Information in a Sample | |
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Designing Experiments to Increase Accuracy | |
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The Matched Pairs Experiment | |
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Some Elementary Experimental Designs | |
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Summary | |
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The Analysis of Variance | |
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Introduction | |
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The Analysis of Variance Procedure | |
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Comparison of More than Two Means: Analysis of Variance for a One-Way Layout | |
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An Analysis of Variance Table for a One-Way Layout | |
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A Statistical Model for the One-Way Layout | |
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Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional) | |
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Estimation in the One-Way Layout | |
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A Statistical Model for the Randomized Block Design | |
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The Analysis of Variance for a Randomized Block Design | |
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Estimation in the Randomized Block Design | |
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Selecting the Sample Size | |
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Simultaneous Confidence Intervals for More than One Parameter | |
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Analysis of Variance Using Linear Models | |
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Summary | |
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Analysis of Categorical Data | |
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A Description of the Experiment | |
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The Chi-Square Test | |
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A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test | |
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Contingency Tables | |
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r [times] c Tables with Fixed Row or Column Totals | |
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Other Applications | |
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Summary and Concluding Remarks | |
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Nonparametric Statistics | |
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Introduction | |
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A General Two-Sample Shift Model | |
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The Sign Test for a Matched Pairs Experiment | |
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The Wilcoxon Signed-Rank Test for a Matched Pairs Experiment | |
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The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples | |
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The Mann-Whitney U Test: Independent Random Samples | |
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The Kruskal-Wallis Test for the One-Way Layout | |
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The Friedman Test for Randomized Block Designs | |
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The Runs Test: A Test for Randomness | |
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Rank Correlation Coefficient | |
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Some General Comments on Nonparametric Statistical Tests | |
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Matrices and Other Useful Mathematical Results | |
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Matrices and Matrix Algebra | |
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Addition of Matrices | |
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Multiplication of a Matrix by a Real Number | |
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Matrix Multiplication | |
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Identity Elements | |
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The Inverse of a Matrix | |
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The Transpose of a Matrix | |
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A Matrix Expression for a System of Simultaneous Linear Equations | |
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Inverting a Matrix | |
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Solving a System of Simultaneous Linear Equations | |
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Other Useful Mathematical Results | |
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Common Probability Distributions, Means, Variances, and Moment-Generating Functions | |
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Discrete Distributions | |
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Continuous Distributions | |
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Tables | |
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Binomial Probabilities | |
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Table of e[superscript -x] | |
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Poisson Probabilities | |
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Normal Curve Areas | |
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Percentage Points of the t Distributions | |
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Percentage Points of the x[superscript 2] Distributions | |
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Percentage Points of the F Distributions | |
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Distribution Function of U | |
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Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test | |
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Distribution of the Total Number of Runs R in Samples of Size (n[subscript 1], n[subscript 2]); P(R [less than or equal] a) | |
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Critical Values of Spearman's Rank Correlation Coefficient | |
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Random Numbers | |
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Answers to Exercises | |
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Index | |