Mathematical Statistics with Applications 7th edition

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• Chapter 1: What Is Statistics?
  • 1: Concept Explorations
  • 1: Precalculus Review
  • 1.1: Introduction
  • 1.2: Characterizing a Set of Measurements: Graphical Methods
  • 1.3: Characterizing a Set of Measurements: Numerical Methods
  • 1.4: How Inferences Are Made
  • 1.5: Theory and Reality
  • 1.6: Summary
  • 1: Supplementary Exercises
  • 1: Concept Questions
  
  
• Chapter 2: Probability
  • 2: Concept Explorations
  • 2: Precalculus Review
  • 2.1: Introduction
  • 2.2: Probability and Inference
  • 2.3: A Review of Set Notation
  • 2.4: A Probabilistic Model for an Experiment: The Discrete Case
  • 2.5: Calculating the Probability of an Event: The Sample-Point Method
  • 2.6: Tools for Counting Sample Points
  • 2.7: Conditional Probability and the Independence of Events
  • 2.8: Two Laws of Probability
  • 2.9: Calculating the Probability of an Event: The Event-Composition Method
  • 2.10: The Law of Total Probability and Bayes' Rule
  • 2.11: Numerical Events and Random Variables
  • 2.12: Random Sampling
  • 2.13: Summary
  • 2: Supplementary Exercises
  • 2: Concept Questions
  
  
• Chapter 3: Discrete Random Variables and Their Probability Distributions
  • 3: Concept Explorations
  • 3: Precalculus and Calculus Review
  • 3.1: Basic Definition
  • 3.2: The Probability Distribution for a Discrete Random Variable
  • 3.3: The Expected Value of a Random Variable or a Function of a Random Variable
  • 3.4: The Binomial Probability Distribution
  • 3.5: The Geometric Probability Distribution
  • 3.6: The Negative Binomial Probability Distribution (Optional)
  • 3.7: The Hypergeometric Probability Distribution
  • 3.8: The Poisson Probability Distribution
  • 3.9: Moments and Moment-Generating Functions
  • 3.10: Probability-Generating Functions (Optional)
  • 3.11: Tchebysheff's Theorem
  • 3.12: Summary
  • 3: Supplementary Exercises
  • 3: Concept Questions
  
  
• Chapter 4: Continuous Variables and Their Probability Distributions
  • 4: Concept Explorations
  • 4: Calculus Review
  • 4.1: Introduction
  • 4.2: The Probability Distribution for a Continuous Random Variable
  • 4.3: Expected Values for Continuous Random Variables
  • 4.4: The Uniform Probability Distribution
  • 4.5: The Normal Probability Distribution
  • 4.6: The Gamma Probability Distribution
  • 4.7: The Beta Probability Distribution
  • 4.8: Some General Comments
  • 4.9: Other Expected Values
  • 4.10: Tchebysheff's Theorem
  • 4.11: Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)
  • 4.12: Summary
  • 4: Supplementary Exercises
  • 4: Concept Questions
  
  
• Chapter 5: Multivariate Probability Distributions
  • 5: Concept Explorations
  • 5: Precalculus and Calculus Review
  • 5.1: Introduction
  • 5.2: Bivariate and Multivariate Probability Distributions
  • 5.3: Marginal and Conditional Probability Distributions
  • 5.4: Independent Random Variables
  • 5.5: The Expected Value of a Function of Random Variables
  • 5.6: Special Theorems
  • 5.7: The Covariance of Two Random Variables
  • 5.8: The Expected Value and Variance of Linear Functions of Random Variables
  • 5.9: The Multinomial Probability Distribution
  • 5.10: The Bivariate Normal Distribution (Optional)
  • 5.11: Conditional Expectations
  • 5.12: Summary
  • 5: Supplementary Exercises
  • 5: Concept Questions
  
  
• Chapter 6: Functions of Random Variables
  • 6: Concept Explorations
  • 6: Precalculus and Calculus Review
  • 6.1: Introduction
  • 6.2: Finding the Probability Distribution of a Function of Random Variables
  • 6.3: The Method of Distribution Functions
  • 6.4: The Method of Transformations
  • 6.5: The Method of Moment-Generating Functions
  • 6.6: Multivariable Transformations Using Jacobians (Optional)
  • 6.7: Order Statistics
  • 6.8: Summary
  • 6: Supplementary Exercises
  • 6: Concept Questions
  
  
• Chapter 7: Sampling Distributions and the Central Limit Theorem
  • 7: Concept Explorations
  • 7: Precalculus Review
  • 7.1: Introduction
  • 7.2: Sampling Distributions Related to the Normal Distribution
  • 7.3: The Central Limit Theorem
  • 7.4: A Proof of the Central Limit Theorem (Optional)
  • 7.5: The Normal Approximation to the Binomial Distribution
  • 7.6: Summary
  • 7: Supplementary Exercises
  • 7: Concept Questions
  • 7: Labs
  
  
• Chapter 8: Estimation
  • 8: Concept Explorations
  • 8: Precalculus and Calculus Review
  • 8.1: Introduction
  • 8.2: The Bias and Mean Square Error of Point Estimators
  • 8.3: Some Common Unbiased Point Estimators
  • 8.4: Evaluating the Goodness of a Point Estimator
  • 8.5: Confidence Intervals
  • 8.6: Large-Sample Confidence Intervals
  • 8.7: Selecting the Sample Size
  • 8.8: Small-Sample Confidence Intervals for μ and μ₁ − μ₂
  • 8.9: Confidence Intervals for σ²
  • 8.10: Summary
  • 8: Supplementary Exercises
  • 8: Concept Questions
  
  
• Chapter 9: Properties of Point Estimators and Methods of Estimation
  • 9: Concept Explorations
  • 9: Precalculus and Calculus Review
  • 9.1: Introduction
  • 9.2: Relative Efficiency
  • 9.3: Consistency
  • 9.4: Sufficiency
  • 9.5: The Rao–Blackwell Theorem and Minimum-Variance Unbiased Estimation
  • 9.6: The Method of Moments
  • 9.7: The Method of Maximum Likelihood
  • 9.8: Some Large-Sample Properties of Maximum-Likelihood Estimators (Optional)
  • 9.9: Summary
  • 9: Supplementary Exercises
  • 9: Concept Questions
  
  
• Chapter 10: Hypothesis Testing
  • 10: Concept Explorations
  • 10: Precalculus Review
  • 10.1: Introduction
  • 10.2: Elements of a Statistical Test
  • 10.3: Common Large-Sample Tests
  • 10.4: Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests
  • 10.5: Relationships Between Hypothesis-Testing Procedures and Confidence Intervals
  • 10.6: Another Way to Report the Results of a Statistical Test: Attained Significance Levels, or p-Values
  • 10.7: Some Comments on the Theory of Hypothesis Testing
  • 10.8: Small-Sample Hypothesis Testing for μ and μ₁ − μ₂
  • 10.9: Testing Hypotheses Concerning Variances
  • 10.10: Power of Tests and the Neyman–Pearson Lemma
  • 10.11: Likelihood Ratio Tests
  • 10.12: Summary
  • 10: Supplementary Exercises
  • 10: Concept Questions
  
  
• Chapter 11: Linear Models and Estimation by Least Squares
  • 11: Concept Explorations
  • 11: Precalculus and Calculus Review
  • 11.1: Introduction
  • 11.2: Linear Statistical Models
  • 11.3: The Method of Least Squares
  • 11.4: Properties of the Least-Squares Estimators: Simple Linear Regression
  • 11.5: Inferences Concerning the Parameters β_i
  • 11.6: Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
  • 11.7: Predicting a Particular Value of Y by Using Simple Linear Regression
  • 11.8: Correlation
  • 11.9: Some Practical Examples
  • 11.10: Fitting the Linear Model by Using Matrices
  • 11.11: Linear Functions of the Model Parameters: Multiple Linear Regression
  • 11.12: Inferences Concerning Linear Functions of the Model Parameters: Multiple Linear Regression
  • 11.13: Predicting a Particular Value of Y by Using Multiple Regression
  • 11.14: A Test for H₀ : β_{g + 1} = β_{g + 2} = … = β_k = 0
  • 11.15: Summary and Concluding Remarks
  • 11: Supplementary Exercises
  • 11: Concept Questions
  
  
• Chapter 12: Considerations in Designing Experiments
  • 12: Concept Explorations
  • 12: Precalculus Review
  • 12.1: The Elements Affecting the Information in a Sample
  • 12.2: Designing Experiments to Increase Accuracy
  • 12.3: The Matched-Pairs Experiment
  • 12.4: Some Elementary Experimental Designs
  • 12.5: Summary
  • 12: Supplementary Exercises
  • 12: Concept Questions
  
  
• Chapter 13: The Analysis of Variance
  • 13: Concept Explorations
  • 13: Precalculus Review
  • 13.1: Introduction
  • 13.2: The Analysis of Variance Procedure
  • 13.3: Comparison of More Than Two Means: Analysis of Variance for a One-Way Layout
  • 13.4: An Analysis of Variance Table for a One-Way Layout
  • 13.5: A Statistical Model for the One-Way Layout
  • 13.6: Proof of Additivity of the Sums of Squares and E(MST) for a One-Way Layout (Optional)
  • 13.7: Estimation in the One-Way Layout
  • 13.8: A Statistical Model for the Randomized Block Design
  • 13.9: The Analysis of Variance for a Randomized Block Design
  • 13.10: Estimation in the Randomized Block Design
  • 13.11: Selecting the Sample Size
  • 13.12: Simultaneous Confidence Intervals for More Than One Parameter
  • 13.13: Analysis of Variance Using Linear Models
  • 13.14: Summary
  • 13: Supplementary Exercises
  • 13: Concept Questions
  • 13: Labs
  
  
• Chapter 14: Analysis of Categorical Data
  • 14: Concept Explorations
  • 14: Precalculus and Calculus Review
  • 14.1: A Description of the Experiment
  • 14.2: The Chi-Square Test
  • 14.3: A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-Fit Test
  • 14.4: Contingency Tables
  • 14.5: r × c Tables with Fixed Row or Column Totals
  • 14.6: Other Applications
  • 14.7: Summary and Concluding Remarks
  • 14: Supplementary Exercises
  • 14: Concept Questions
  
  
• Chapter 15: Nonparametric Statistics
  • 15: Concept Explorations
  • 15: Precalculus Review
  • 15.1: Introduction
  • 15.2: A General Two-Sample Shift Model
  • 15.3: The Sign Test for a Matched-Pairs Experiment
  • 15.4: The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment
  • 15.5: Using Ranks for Comparing Two Population Distributions: Independent Random Samples
  • 15.6: The Mann–Whitney U Test: Independent Random Samples
  • 15.7: The Kruskal–Wallis Test for the One-Way Layout
  • 15.8: The Friedman Test for Randomized Block Designs
  • 15.9: The Runs Test: A Test for Randomness
  • 15.10: Rank Correlation Coefficient
  • 15.11: Some General Comments on Nonparametric Statistical Tests
  • 15: Supplementary Exercises
  • 15: Concept Questions
  
  
• Chapter 16: Introduction to Bayesian Methods for Inference
  • 16: Concept Explorations
  • 16: Precalculus and Calculus Review
  • 16.1: Introduction
  • 16.2: Bayesian Priors, Posteriors, and Estimators
  • 16.3: Bayesian Credible Intervals
  • 16.4: Bayesian Tests of Hypotheses
  • 16.5: Summary and Additional Comments
  • 16: Concept Questions
  
  
• Chapter PJT: Project
  • PJT.1: Project