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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 | |