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| What Is Statistics? 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 Methods | |
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| The Law of Total Probability and Bayes's 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 Discrete Random Variable | |
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| The Expected Value of Random Variable or a Function of 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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| 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 Continuous Random Variable | |
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| The Expected Value for Continuous Random Variable | |
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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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| 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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| Introductions | |
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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 Methods of Transformations | |
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| Multivariable Transformations Using Jacobians | |
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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 Distributions | |
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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 Point Estimator | |
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| Confidence Intervals | |
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| Large-Sample Confidence Intervals Selecting the Sample Size | |
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| Small-Sample Confidence Intervals for u and u1-u2 | |
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| Confidence Intervals for o2 | |
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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 u and u1-u2 | |
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| Testing Hypotheses Concerning Variances | |
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| Power of Test and the Neyman-Pearson Lemma | |
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| Likelihood Ration Test | |
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| Summary | |
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| Linear Models and Estimation by Least Sq | |