Mathematical Statistics with Applications 8th edition

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• Chapter 1: What Is Statistics?
  • 1: Concept Explorations
  • 1: Precalculus Review
  • 1.1: Population and Data
  • 1.2: Characterizing a Set of Measurements: Graphical Methods
  • 1.3: Characterizing a Set of Measurements: Numerical Methods
  • 1.4: Making Statistical Inference
  • 1: Supplementary Exercises
  
  
• Chapter 2: Probability
  • 2: Concept Explorations
  • 2: Precalculus Review
  • 2.1: Interpreting Probabilities
  • 2.2: A Review of Set Notation
  • 2.3: A Probabilistic Model for an Experiment: The Discrete Case
  • 2.4: Calculating the Probability of an Event: The Sample-Point Method
  • 2.5: Tools for Counting Sample Points
  • 2.6: Conditional Probability and the Independence of Events
  • 2.7: Two Laws of Probability
  • 2.8: Calculating the Probability of an Event: The Event-Composition Method
  • 2.9: The Law of Total Probability and Bayes' Rule
  • 2: Supplementary Exercises
  
  
• Chapter 3: Discrete Random Variables and Their Probability Distributions
  • 3: Concept Explorations
  • 3: Precalculus and Calculus Review
  • 3.1: Random Variables
  • 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 Bernoulli and Binomial Probability Distributions
  • 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: Chebyshev's Inequality for Discrete Random Variables
  • 3: Supplementary Exercises
  
  
• Chapter 4: Continuous Variables and Their Probability Distributions
  • 4: Concept Explorations
  • 4: Calculus Review
  • 4.1: The Probability Distribution for a Continuous Random Variable
  • 4.2: Expected Values for Continuous Random Variables
  • 4.3: The Uniform Probability Distribution
  • 4.4: The Normal Probability Distribution
  • 4.5: The Gamma Probability Distribution
  • 4.6: The Beta Probability Distribution
  • 4.7: Moments and Moment-Generating Functions for Continuous Random Variables
  • 4.8: Chebyshev's Inequality for Continuous Random Variables
  • 4.9: Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional)
  • 4: Supplementary Exercises
  
  
• Chapter 5: Multivariate Probability Distributions
  • 5: Concept Explorations
  • 5: Precalculus and Calculus Review
  • 5.1: Bivariate and Multivariate Probability Distributions
  • 5.2: Marginal and Conditional Probability Distributions
  • 5.3: Independent Random Variables
  • 5.4: The Expected Value of a Function of Random Variables
  • 5.5: The Covariance of Two Random Variables
  • 5.6: The Expected Value and Variance of Linear Functions of Random Variables
  • 5.7: The Multinomial Probability Distribution
  • 5.8: The Bivariate Normal Distribution (Optional)
  • 5.9: Conditional Expectations
  • 5: Supplementary Exercises
  
  
• Chapter 6: Functions of Random Variables
  • 6: Concept Explorations
  • 6: Precalculus and Calculus Review
  • 6.1: Transformations Using the Cumulative Distribution Function
  • 6.2: Density Transformations via Change of Variables
  • 6.3: Transformations of Moment-Generating Functions
  • 6.4: Multivariate Transformations (Optional)
  • 6: Supplementary Exercises
  
  
• Chapter 7: Sampling Distributions
  • 7: Concept Explorations
  • 7: Precalculus Review
  • 7.1: Basic Sampling Statistics
  • 7.2: Sampling Distributions Related to Normal Data
  • 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: Order Statistics
  • 7: Supplementary Exercises
  • 7: Labs
  
  
• Chapter 8: Estimation
  • 8: Concept Explorations
  • 8: Precalculus and Calculus Review
  • 8.1: The Bias and Mean Square Error of Point Estimators
  • 8.2: Unbiased Point Estimators on Mean and Proportions
  • 8.3: Confidence Intervals
  • 8.4: Large-Sample Confidence Intervals
  • 8.5: Selecting the Sample Size
  • 8.6: Small-Sample Confidence Intervals for μ and μ₁ − μ₂
  • 8.7: Confidence Intervals for σ²
  • 8: Supplementary Exercises
  
  
• Chapter 9: Properties of Point Estimators
  • 9: Concept Explorations
  • 9: Precalculus and Calculus Review
  • 9.1: Relative Efficiency
  • 9.2: Consistency
  • 9.3: Sufficiency
  • 9.4: Uniformly Minimum Variance Unbiased Estimators
  • 9.5: The Method of Moments
  • 9.6: The Method of Maximum Likelihood
  • 9.7: Large-Sample Confidence Intervals Based on Maximum-Likelihood Estimators (Optional)
  • 9: Supplementary Exercises
  
  
• Chapter 10: Hypothesis Testing
  • 10: Concept Explorations
  • 10: Precalculus Review
  • 10.1: Elements of a Statistical Test
  • 10.2: Common Large-Sample Tests
  • 10.3: Calculating Type II Error Probabilities and Finding the Sample Size for Z Tests
  • 10.4: Relationships Between Hypothesis-Testing Procedures and Confidence Intervals
  • 10.5: Another Way to Report the Results of a Statistical Test: p-Values
  • 10.6: Some Comments on the Theory of Hypothesis Testing
  • 10.7: Small-Sample Hypothesis Testing for μ and μ₁ − μ₂
  • 10.8: Testing Hypotheses Concerning Variances
  • 10.9: Power of Tests and the Neyman–Pearson Lemma
  • 10.10: Likelihood Ratio Tests
  • 10: Supplementary Exercises
  
  
• Chapter 11: Linear Models and Estimation by Least Squares
  • 11: Concept Explorations
  • 11: Precalculus and Calculus Review
  • 11.1: Linear Statistical Models
  • 11.2: The Method of Least Squares
  • 11.3: Properties of the Least-Squares Estimators: Simple Linear Regression
  • 11.4: Inferences Concerning the Parameters β_i
  • 11.5: Inferences Concerning Linear Functions of the Model Parameters: Simple Linear Regression
  • 11.6: Predicting a Particular Value of Y by Using Simple Linear Regression
  • 11.7: Checking Model Assumptions
  • 11.8: Correlation
  • 11.9: Transformations
  • 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: Supplementary Exercises
  
  
• Chapter 12: Experimental Designs
  • 12: Concept Explorations
  • 12: Precalculus Review
  • 12.1: Sampling Information
  • 12.2: Designing Experiments to Increase Accuracy
  • 12.3: The Matched-Pairs Experiment
  • 12.4: Some Elementary Experimental Designs
  • 12: Supplementary Exercises
  
  
• Chapter 13: The Analysis of Variance
  • 13: Concept Explorations
  • 13: Precalculus Review
  • 13.1: ANOVA to Compare Two Means
  • 13.2: ANOVA for Three or More Means
  • 13.3: A Statistical Model for the One-Way Layout
  • 13.4: Estimation in the One-Way Layout
  • 13.5: A Statistical Model for the Randomized Block Design
  • 13.6: The Analysis of Variance for a Randomized Block Design
  • 13.7: Estimation in the Randomized Block Design
  • 13.8: Selecting the Sample Size
  • 13.9: Simultaneous Confidence Intervals Using the Bonferroni Adjustment
  • 13.10: Analysis of Variance Using Linear Models
  • 13: Supplementary Exercises
  • 13: Labs
  
  
• Chapter 14: Analysis of Categorical Data
  • 14: Concept Explorations
  • 14: Precalculus and Calculus Review
  • 14.1: The Chi-Square Test
  • 14.2: Chi-Square Test of Independence
  • 14.3: Chi-Square Test of Homogeneity
  • 14.4: Permutation Tests for Small Counts
  • 14: Supplementary Exercises
  
  
• Chapter 15: Nonparametric Statistics
  • 15: Concept Explorations
  • 15: Precalculus Review
  • 15.1: The Sign Test for a Matched-Pairs Experiment
  • 15.2: The Wilcoxon Signed-Rank Test for a Matched-Pairs Experiment
  • 15.3: The Wilcoxon–Mann–Whitney Test Comparing Two Independent Samples
  • 15.4: The Kruskal–Wallis Test for the One-Way Layout
  • 15.5: The Friedman Test for Randomized Block Designs
  • 15.6: The Runs Test: A Test for Randomness
  • 15.7: Rank Correlation Coefficient
  • 15: Supplementary Exercises
  
  
• Chapter 16: Introduction to Bayesian Methods for Inference
  • 16: Concept Explorations
  • 16: Precalculus and Calculus Review
  • 16.1: Bayesian Priors, Posteriors, and Estimators
  • 16.2: Bayesian Credible Intervals
  • 16.3: Bayesian Tests of Hypotheses
  
  
• Chapter PJT: Project
  • PJT.1: Project