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Preface | |

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Preface to First Edition | |

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Introduction to Statistical Science | |

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The Scientific Method: A Process for Learning | |

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The Role of Statistics in the Scientific Method | |

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Main Approaches to Statistics | |

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Purpose and Organization of This Text | |

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Scientific Data Gathering | |

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Sampling from a Real Population | |

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Observational Studies and Designed Experiments | |

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Monte Carlo Exercises | |

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Displaying and Summarizing Data | |

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Graphically Displaying a Single Variable | |

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Graphically Comparing Two Samples | |

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Measures of Location | |

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Measures of Spread | |

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Displaying Relationships Between Two or More Variables | |

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Measures of Association for Two or More Variables | |

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Exercises | |

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Logic, Probability, and Uncertainty | |

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Deductive Logic and Plausible Reasoning | |

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Probability | |

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Axioms of Probability | |

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Joint Probability and Independent Events | |

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Conditional Probability | |

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Bayes' Theorem | |

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Assigning Probabilities | |

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Odds Ratios and Bayes Factor | |

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Beat the Dealer | |

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Exercises | |

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Discrete Random Variables | |

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Discrete Random Variables | |

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Probability Distribution of a Discrete Random Variable | |

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Binomial Distribution | |

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Hypergeometric Distribution | |

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Poisson Distribution | |

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Joint Random Variables | |

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Conditional Probability for Joint Random Variables | |

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Exercises | |

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Bayesian Inference for Discrete Random Variables | |

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Two Equivalent Ways of Using Bayes' Theorem | |

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Bayes' Theorem for Binomial with Discrete Prior | |

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Important Consequences of Bayes' Theorem | |

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Bayes' theorem for Poisson with Discrete Prior | |

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Exercises | |

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Computer Exercises | |

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Continuous Random Variables | |

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Probability Density Function | |

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Some Continuous Distributions | |

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Joint Continuous Random Variables | |

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Joint Continuous and Discrete Random Variables | |

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Exercises | |

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Bayesian Inference for Binomial Proportion | |

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Using a Uniform Prior | |

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Using a Beta Prior | |

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Choosing Your Prior | |

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Summarizing the Posterior Distribution | |

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Estimating the Proportion | |

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Bayesian Credible Interval | |

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Exercises | |

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Computer Exercises | |

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Comparing Bayesian and Frequentist Inferences for Proportion | |

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Frequentist Interpretation of Probability and Parameters | |

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Point Estimation | |

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Comparing Estimators for Proportion | |

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Interval Estimation | |

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Hypothesis Testing | |

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Testing a OneSided Hypothesis | |

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Testing a TwoSided Hypothesis | |

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Exercises | |

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Carlo Exercises | |

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Bayesian Inference for Poisson | |

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Some Prior Distributions for Poisson | |

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Inference for Poisson Parameter | |

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Exercises | |

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Computer Exercises | |

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Bayesian Inference for Normal Mean | |

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Bayes' Theorem for Normal Mean with a Discrete Prior | |

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Bayes' Theorem for Normal Mean with a Continuous Prior | |

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Choosing Your Normal Prior | |

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Bayesian Credible Interval for Normal Mean | |

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Predictive Density for Next Observation | |

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Exercises | |

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Computer Exercises | |

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Comparing Bayesian and Frequentist Inferences for Mean | |

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Comparing Frequentist and Bayesian Point Estimators | |

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Comparing Confidence and Credible Intervals for Mean | |

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Testing a OneSided Hypothesis about a Normal Mean | |

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Testing a TwoSided Hypothesis about a Normal Mean | |

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Exercises | |

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Bayesian Infer | |