Introduction to Bayesian statistics 5.5 Poisson DistributionCharacteristics of the Poisson Distribution; 5.6 Joint Random Variables; Independent Random Variables; 5.7 Conditional Probability for Joint Random Variables; Exercises; 6 Bayesian Inference for Discrete Random Variables; 6.1 Two Equivalent Ways of Using Bayes Theorem; 6.2 Bayes Theorem for Binomial with Discrete Prior; Setting up the Table for Bayes Theorem on Binomial with Discrete Prior; 6.3 Important Consequences of Bayes Theorem; 6.4 Bayes Theorem for Poisson with Discrete Prior; Setting up the Table for Bayes Theorem on Poisson with Discrete Prior INTRODUCTION TO BAYESIAN STATISTICS; Contents; Preface; Changes in the Third Edition; Our Perspective on Bayesian Statistics; Acknowledgments; 1 Introduction to Statistical Science; 1.1 The Scientific Method: A Process for Learning; 1.2 The Role of Statistics in the Scientific Method; 1.3 Main Approaches to Statistics; Frequentist Approach to Statistics; Bayesian Approach to Statistics; Monte Carlo Studies; 1.4 Purpose and Organization of This Text; 2 Scientific Data Gathering; 2.1 Sampling from a Real Population; Simple Random Sampling (without Replacement); Stratified Random Sampling Interquartile Range: Advantages and DisadvantagesVariance: Advantages and Disadvantages; Standard Deviation: Advantages and Disadvantages; 3.5 Displaying Relationships Between Two or More Variables; Scatterplot; Scatterplot Matrix; 3.6 Measures of Association for Two or More Variables; Covariance and Correlation between Two Variables; Exercises; 4 Logic Probability and Uncertainty; 4.1 Deductive Logic and Plausible Reasoning; Desired Properties of Plausibility Measures; 4.2 Probability; 4.3 Axioms of Probability; 4.4 Joint Probability and Independent Events; 4.5 Conditional Probability Non sampling Errors in Sample SurveysRandomized Response Methods; 2.2 Observational Studies and Designed Experiments; Observational Study; Designed Experiment; Monte Carlo Exercises; 3 Displaying and Summarizing Data; 3.1 Graphically Displaying a Single Variable; Dotplot; Boxplot (Box and Whisker Plot); Stem and Leaf Diagram; Frequency Table; Histogram; Cumulative Frequency Polygon; 3.2 Graphically Comparing Two Samples; 3.3 Measures of Location; Mean: Advantages and Disadvantages; Median: Advantages and Disadvantages; 3.4 Measures of Spread; Range: Advantage and Disadvantage 4.6 Bayes TheoremBayes Theorem: The Key to Bayesian Statistics; 4.7 Assigning Probabilities; 4.8 Odds and Bayes Factor; Bayes Factor (B); 4.9 Beat the Dealer; Exercises; 5 Discrete Random Variables; 5.1 Discrete Random Variables; 5.2 Probability Distribution of a Discrete Random Variable; Expected Value of a Discrete Random Variable; The Variance of a Discrete Random Variable; The Mean and Variance of a Linear Function of a Random Variable; 5.3 Binomial Distribution; Characteristics of the Binomial Distribution; 5.4 Hypergeometric Distribution; Probability Function of Hypergeometric