Mathematical Statistics with Applications 7th Edition by Dennis Wackerly ISBN 1111798788 9781111798789

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ISBN 10: 1111798788
ISBN 13: 9781111798789
Author: Dennis Wackerly

In their bestselling title MATHEMATICAL STATISTICS WITH APPLICATIONS, premiere authors Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer present a solid foundation in statistical theory while conveying the relevance and importance of the theory in solving practical problems in the real world. The authors’ use of practical applications and excellent exercises helps students discover the nature of statistics and understand its essential role in scientific research.

Mathematical Statistics with Applications 7th Table of contents:

Ch 1: What Is Statistics?

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

Ch 1: References and Further Readings

Ch 1: Supplementary Exercises

Ch 2: Probability

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

Ch 2: References and Further Readings

Ch 2: Supplementary Exercises

Ch 3: Discrete Random Variables and Their Probability Distributions

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

Ch 3: References and Further Readings

Ch 3: Supplementary Exercises

Ch 4: Continuous Variables and Their Probability Distributions

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

Ch 4: References and Further Readings

Ch 4: Supplementary Exercises

Ch 5: Multivariate Probability Distributions

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

Ch 5: References and Further Readings

Ch 5: Supplementary Exercises

Ch 6: Functions of Random Variables

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

Ch 6: References and Further Readings

Ch 6: Supplementary Exercises

Ch 7: Sampling Distributions and the Central Limit Theorem

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

Ch 7: References and Further Readings

Ch 7: Supplementary Exercises

Ch 8: Estimation

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 σ 2

8.10: Summary

Ch 8: References and Further Readings

Ch 8: Supplementary Exercises

Ch 9: Properties of Point Estimators and Methods of Estimation

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

Ch 9: References and Further Readings

Ch 10: Supplementary Exercises

Ch 10: Hypothesis Testing

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-Va

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

Ch 10: References and Further Readings

Ch 10: Supplementary Exercises

Ch 11: Linear Models and Estimation by Least Squares

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 βi

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: βg+1 = βg+2 = ··· = βk = 0

11.15: Summary and Concluding Remarks

Ch 11: References and Further Readings

Ch 11: Supplementary Exercises

Ch 12: Considerations in Designing Experiments

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

Ch 12: References and Further Readings

Ch 12: Supplementary Exercises

Ch 13: The Analysis of Variance

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

Ch 13: References and Further Readings

Ch 13: Supplementary Exercises

Ch 14: Analysis of Categorical Data

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

Ch 14: References and Further Readings

Ch 14: Supplementary Exercises

Ch 15: Nonparametric Statistics

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

Ch 15: References and Further Readings

Ch 15: Supplementary Exercises

Ch 16: Introduction to Bayesian Methods for Inference

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

Ch 16: References and Further Readings

Appendix 1: Matrices and Other Useful Mathematical Results

Appendix 2: Common Probability Distributions, Means, Variances, and Moment-Generating Functions

Appendix 3: Tables

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