Probability and Statistics for Engineers and Scientists / Edition 9

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This classic text provides a rigorous introduction to basic probability theory and statistical inference, with a unique balance of theory and methodology. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. This revision focuses on improved clarity and deeper understanding.

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Product Details

  • ISBN-13: 9780321629111
  • Publisher: Pearson
  • Publication date: 1/10/2011
  • Edition description: New Edition
  • Edition number: 9
  • Pages: 816
  • Sales rank: 179,333
  • Product dimensions: 7.50 (w) x 9.10 (h) x 1.30 (d)

Meet the Author

Raymond H Myers is currently Professor Emeritus of statistics at Virginia Tech. He received his Masters and Ph.D. from Virginia Tech in statistics and his BS in chemical engineering. His major areas of interest are linear models, design of experiments, and response surface methodology. He has authored or co-authored six statistics texts that were published in fifteen separate editions and in several foreign languages.

He has received numerous teaching awards and in 1985 he was selected “Professor of the Year” in the state of Virginia by the Council on the Advancement and Support of Education. He was elected Fellow of ASA in 1974. In 1999 he was given the Shewhart Award for lifetime contributions in statistics and quality control by the American Society of Quality.

Sharon L Myers is currently Professor Emeritus of mathematics and statistics at Radford University. She received her MS in statistics from Virginia Tech. Her areas of interest are statistical computing, regression analysis, and response surface methodology. She has co-authored three editions of “Probability & Statistics for Engineers & Scientists”. She was the assistant director of the statistical consulting center at Virginia Tech for 15 years and the director of the statistical consulting center at Radford University for 7 years.

Keying Ye, University of Texas at San Antonio

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Table of Contents


1. Introduction to Statistics and Data Analysis

1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability

1.2 Sampling Procedures; Collection of Data

1.3 Measures of Location: The Sample Mean and Median


1.4 Measures of Variability


1.5 Discrete and Continuous Data

1.6 Statistical Modeling, Scientific Inspection, and Graphical Methods 19

1.7 General Types of Statistical Studies: Designed Experiment,

Observational Study, and Retrospective Study


2. Probability

2.1 Sample Space

2.2 Events


2.3 Counting Sample Points


2.4 Probability of an Event

2.5 Additive Rules


2.6 Conditional Probability, Independence and Product Rules


2.7 Bayes’ Rule


Review Exercises

2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

3. Random Variables and Probability Distributions

3.1 Concept of a Random Variable

3.2 Discrete Probability Distributions

3.3 Continuous Probability Distributions


3.4 Joint Probability Distributions


Review Exercises

3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

4. Mathematical Expectation

4.1 Mean of a Random Variable


4.2 Variance and Covariance of Random Variables


4.3 Means and Variances of Linear Combinations of Random Variables 127

4.4 Chebyshev’s Theorem


Review Exercises

4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

5. Some Discrete Probability Distributions

5.1 Introduction and Motivation

5.2 Binomial and Multinomial Distributions


5.3 Hypergeometric Distribution


5.4 Negative Binomial and Geometric Distributions

5.5 Poisson Distribution and the Poisson Process


Review Exercises

5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

6. Some Continuous Probability Distributions

6.1 Continuous Uniform Distribution

6.2 Normal Distribution

6.3 Areas under the Normal Curve

6.4 Applications of the Normal Distribution


6.5 Normal Approximation to the Binomial


6.6 Gamma and Exponential Distributions

6.7 Chi-Squared Distribution

6.8 Beta Distribution

6.9 Lognormal Distribution (Optional)

6.10 Weibull Distribution (Optional)


Review Exercises

6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

7. Functions of Random Variables (Optional)

7.1 Introduction

7.2 Transformations of Variables

7.3 Moments and Moment-Generating Functions


8. Sampling Distributions and More Graphical Tools

8.1 Random Sampling and Sampling Distributions

8.2 Some Important Statistics


8.3 Sampling Distributions

8.4 Sampling Distribution of Means and the Central Limit Theorem


8.5 Sampling Distribution of S 2

8.6 t-Distribution

8.7 F-Distribution

8.8 Quantile and Probability Plots


Review Exercises

8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

9. One- and Two-Sample Estimation Problems

9.1 Introduction

9.2 Statistical Inference

9.3 Classical Methods of Estimation

9.4 Single Sample: Estimating the Mean

9.5 Standard Error of a Point Estimate

9.6 Prediction Intervals

9.7 Tolerance Limits


9.8 Two Samples: Estimating the Difference Between Two Means

9.9 Paired Observations


9.10 Single Sample: Estimating a Proportion

9.11 Two Samples: Estimating the Difference between Two Proportions


9.12 Single Sample: Estimating the Variance

9.13 Two Samples: Estimating the Ratio of Two Variances


9.14 Maximum Likelihood Estimation (Optional)


Review Exercises

9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

10. One- and Two-Sample Tests of Hypotheses

10.1 Statistical Hypotheses: General Concepts

10.2 Testing a Statistical Hypothesis

10.3 The Use of P-Values for Decision Making in Testing Hypotheses


10.4 Single Sample: Tests Concerning a Single Mean

10.5 Two Samples: Tests on Two Means

10.6 Choice of Sample Size for Testing Means

10.7 Graphical Methods for Comparing Means


10.8 One Sample: Test on a Single Proportion

10.9 Two Samples: Tests on Two Proportions


10.10 One- and Two-Sample Tests Concerning Variances


10.11 Goodness-of-Fit Test

10.12 Test for Independence (Categorical Data)

10.13 Test for Homogeneity

10.14 Two-Sample Case Study


Review Exercises

10.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

11. Simple Linear Regression and Correlation

11.1 Introduction to Linear Regression

11.2 The Simple Linear Regression Model

11.3 Least Squares and the Fitted Model


11.4 Properties of the Least Squares Estimators

11.5 Inferences Concerning the Regression Coefficients

11.6 Prediction


11.7 Choice of a Regression Model

11.8 Analysis-of-Variance Approach

11.9 Test for Linearity of Regression: Data with Repeated Observations 416


11.10 Data Plots and Transformations

11.11 Simple Linear Regression Case Study

11.12 Correlation


Review Exercises

11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

12. Multiple Linear Regression and Certain Nonlinear Regression Models

12.1 Introduction

12.2 Estimating the Coefficients

12.3 Linear Regression Model Using Matrices


12.4 Properties of the Least Squares Estimators

12.5 Inferences in Multiple Linear Regression


12.6 Choice of a Fitted Model through Hypothesis Testing

12.7 Special Case of Orthogonality (Optional)


12.8 Categorical or Indicator Variables


12.9 Sequential Methods for Model Selection

12.10 Study of Residuals and Violation of Assumptions

12.11 Cross Validation, Cp , and Other Criteria for Model Selection


12.12 Special Nonlinear Models for Nonideal Conditions


Review Exercises

12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

13. One-Factor Experiments: General

13.1 Analysis-of-Variance Technique

13.2 The Strategy of Experimental Design

13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA)

13.4 Tests for the Equality of Several Variances


13.5 Multiple Comparisons


13.6 Comparing a Set of Treatments in Blocks

13.7 Randomized Complete Block Designs

13.8 Graphical Methods and Model Checking

13.9 Data Transformations In Analysis of Variance)


13.10 Random Effects Models

13.11 Case Study


Review Exercises

13.12 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

14. Factorial Experiments (Two or More Factors)

14.1 Introduction

14.2 Interaction in the Two-Factor Experiment

14.3 Two-Factor Analysis of Variance


14.4 Three-Factor Experiments


14.5 Factorial Experiments for Random Effects and Mixed Models


Review Exercises

14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

15. 2 k Factorial Experiments and Fractions

15.1 Introduction

15.2 The 2 k Factorial: Calculation of Effects and Analysis of Variance 598

15.3 Nonreplicated 2 k Factorial Experiment


15.4 Factorial Experiments in a Regression Setting

15.5 The Orthogonal Design


15.6 Fractional Factorial Experiments

15.7 Analysis of Fractional Factorial Experiments


15.8 Higher Fractions and Screening Designs

15.9 Construction of Resolution III and IV Designs

15.10 Other Two-Level Resolution III Designs; The Plackett-Burman Designs

15.11 Introduction to Response Surface Methodology

15.12 Robust Parameter Design


Review Exercises

15.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

16. Nonparametric Statistics

16.1 Nonparametric Tests

16.2 Signed-Rank Test


16.3 Wilcoxon Rank-Sum Test

16.4 Kruskal-Wallis Test


16.5 Runs Test

16.6 Tolerance Limits

16.7 Rank Correlation Coefficient


Review Exercises

17. Statistical Quality Control

17.1 Introduction

17.2 Nature of the Control Limits

17.3 Purposes of the Control Chart

17.4 Control Charts for Variables

17.5 Control Charts for Attributes

17.6 Cusum Control Charts

Review Exercises

18 Bayesian Statistics

18.1 Bayesian Concepts

18.2 Bayesian Inferences

18.3 Bayes Estimates Using Decision Theory Framework



A. Statistical Tables and Proofs

B. Answers to Odd-Numbered Non-Review Exercises


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Goals, Approach and Mathematical Level

The seventh edition emphasizes and illustrates the use of probabilistic models and statistical methodology that is employed in countless applications in all areas of science and engineering. There remains an important balance between theory and methodology that is featured in the text. We do not avoid the use of some theory but our goal is to let the mathematics provide insight rather than be a distraction. We feel that engineers and scientists are trained in mathematics and thus the providing of mathematical support when needed keeps the pedagogy from becoming a series of illustrated recipes in which the concepts are not understood and could never be applied or extended by the student except within very narrow bounds.

The text contains an abundance of exercises in which the methodology discussed is illustrated by the use of real-life scientific scenarios and data sets. The complete set of data files which accompany the text are available for download from the text companion website, located at our site. Though we attempt to appeal to engineers, the exercises are not confined to engineering applications. The student is exposed to problems encountered in many sciences including social sciences and biomedical applications. The motivation here stems from the fact that trained engineers are more and more becoming exposed to nontraditional settings, including areas like bioinformatics and bioengineering.

While we do let calculus play an important role but it should be noted that its use is confined to elementary probability theory and properties of probability distributions (Chapters 3, 4, 6, and 7). In addition, a modest amount ofmatrix algebra is used to support the linear regression material in Chapters 11 and 12. This is despite the fact that an "optional" section appears in Chapter 11 that includes the development of the multiple linear regression model with more substantive use of matrices. The student who uses this text should have completed one semester or two quarters of differential and integral calculus. An exposure to matrix algebra would be helpful but not necessary if the course content excludes the aforementioned optional section.

Content and Course Planning

The text is designed for either a one or two semester course. A reasonable curriculum for a one semester course might include Chapters 1 through 10. One may even choose to teach an early portion of Chapter 11 in order to introduce the student to the concept of simple linear regression. Chapter 1 is an overview of statistical inference, sampling and data analysis. Indeed, some very rudimentary aspects of experimental design are included, along with an appreciation of graphics and certain vital characteristics of data collection. Chapters 2, 3, and 4 deal with basic probability and discrete and continuous random variables. Chapters 5 and 6 cover specific discrete and continuous distributions with illustrations of their use and relationships among them. Chapter 7 deals with transformations of random variables. This chapter is listed as "optional" and would only be covered in a more theoretical course. This chapter is clearly the most mathematical chapter in the text. Chapter 8 includes additional material on graphical methods as well as an introduction to the notion of a sampling distribution. The t and F distributions are introduced along with motivation regarding their use in chapters that follow. Chapters 9 and 10 contain material on one and two sample point and interval estimation and hypothesis testing. The flexibility in a single semester course lies in the option of exclusion of Chapter 7 as well as teaching only a subset of the several specific discrete and continuous distributions discussed and illustrated in Chapters 5 and 6. There is additional flexibility involved in dealing with Chapter 9 where maximum likelihood and Bayes estimation are covered in detail. An instructor may decide to give only a cursory development of one or both of these topics. In addition, estimation in Chapter 9 includes new material on prediction intervals and tolerance intervals along with a thorough discussion on the distinction among them, with examples. Flexibility may be exercised here.

Chapters 11-17 contain ample material for a second semester of a two-semester course. Chapters 11 and 12 cover simple and multiple linear regression respectively. However, Chapter 12 contains new material that deals with special nonlinear models involved when one deals with nonnormal responses. As a result, logistic and Poisson regression are treated along with important practical illustrations. This in addition to new material in categorical variable regression again provides considerable flexibility for the instructor in his or her treatment of regression. The treatment of regression in this text is extensive and many special regression topics in Chapter 12 are self-contained. Chapters 13 through 17 contain topics in analysis of variance, design of experiments, nonparametric statistics, and quality control.

Case Studies and Computer Software

As in previous editions there are many case studies that demonstrate statistical analysis of interesting real-life data sets. In most cases graphical techniques are used. These case studies are featured in two sample hypothesis testing, multiple linear regression, analysis of variance, and the analysis of 2-level experimental designs. Where appropriate, the use of residual plots, quantile plots, and normal probability plots are described in the analysis. Computer output is used for illustration purposes for these case studies and for other examples in the text. In that regard both SAS and MINITAB are featured. We have always felt that the experience of reading computer printout is invaluable to the student even if the package or packages featured in the text are not what is used by the instructor. Exposure to more than one type of software can broaden the experience base for the student. There is certainly no reason to believe that the software in the course is that which he or she will be called upon to use in practice.

New To This Edition

  1. Chapter 1 has been revised and expanded. Even more emphasis has been placed on the concept of variability. Much of the material on graphical methods in other chapters was moved (where appropriate) to Chapter 1 and is now allowed to flow as illustrative technology with the material on descriptive statistics. We have placed more emphasis in Chapter 1 on a discussion of the necessary role of probability in the "bottom line" provided by data analysis tools. Though much of Chapter 1 is overview, we prepare the student via examples with the notion of a P-value which will be so important in later chapters. In addition, more exercises are added in this chapter to cover the new or transferred material.
  2. More and better examples are given in nearly all chapters. This is a new effort to illustrate with better scientific applications.
  3. Chapter 9 contains new material on Bayesian statistics with additional examples. A section on prediction intervals is given as indicated earlier. Great pains are taken to distinguish among confidence intervals, tolerance intervals, and now, prediction intervals. We find that many students (and practitioners) struggle with these concepts.
  4. Though P-values were introduced several editions earlier, more and better discussion of their interpretation is given early in Chapter 10 on hypothesis testing.
  5. Major changes appear in Chapters 11 and 12 on regression analysis. Simple linear regression contains a more thorough discussion of the meaning of the model asp well as the concept of least squares estimation. These explanations, replete with improved graphics, give the reader a clearer understanding of what regression is all about. Also new and better examples and exercises are given. The discussion of data transformation is also enhanced. Chapter 12 contains two major new topics. One of them is the use of categorical or indicator variables. The other is the introduction of two important nonlinear models for nonnormal responses-logistic regression and Poisson regression. These are accompanied by an explanatory account of how frequently nonnormal responses are encountered in practice. These developments are not overly mathematical but rather highlight examples of their use. Industrial, biological, and biomedical examples are discussed. Chapters 11, 12, and 13 have been "trimmed" to a certain extent by the elimination of certain computational drudgery that has no current pedagogic merit. For example, the development of the normal equations in multiple regression is outlined without the concern for certain laborious computations that are handled by computer software. In addition, in Chapters 13 and 14 the use of so-called computational formulae involving treatment and grand totals, results that bring very little in the way of concept understanding, have been removed. This allows for a more streamlined discussion of ANOVA.
  6. New and better ANOVA examples are included.
  7. New and better examples are given in Chapter 15 on two level factorial and fractional factorial experiments. Soiree of these deal with the very important and timely use of semiconductor manufacturing.
  8. We have made use of much additional highlighting of important material through the use of "boxing in" important results and the use of subsections. We feel that continual page after page of dry text is unattractive, and these reminders of transition to a different or new concept makes for easier learning.

Available Supplements

  1. Student Solutions Manual (0-13-041537-5) Contains carefully-worked solutions to all odd-numbered exercises.
  2. Instructor's Solutions Manual (0-13-041536-7) Contains carefully-worked solutions to all exercises.
  3. Companion Website: Available free to all adopters, the companion website can be found at our site, and includes: the data sets from the book in a downloadable format, MINITAB projects, syllabus manager, hints, quizzes, objectives, and destinations.
  4. SPSS 10.0 Windows Full Student Version (0-13-028040-2)
  5. 2000 MINITAB Student Version Integrated CD (0-13-026082-7)


We are indeed indebted to those colleagues who reviewed the sixth edition and provided many helpful suggestions for this edition. They are: Ruxu Du, University of Miami; Nirmal Devi, Embry Riddle; Judith Miller, Georgetown University; Stephanie Edwards, Bemidji State University. We would like to thank personnel at the Virginia Tech Statistical Consulting Center. The consulting center was the source of many real-life data sets. In addition we thank Linda Seawell who worked hard in the typing and preparation of the manuscript.


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