# Probability & Statistics for Engineers & Scientists, 9th edition

Published by Pearson (March 7, 2016) © 2017

**Ronald E. Walpole**Roanoke College , Virginia Polytechnic Institute**Raymond H. Myers**Virginia Polytechnic Institute**Sharon L. Myers****Keying E. Ye**University of Texas at San Antonio , Virginia Polytechnic Institute & State University

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## MyLab

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For junior/senior-level courses in Probability and Statistics.

### Applies probability and statistics to engineering, science and computer science

**Probability & Statistics for Engineers & Scientists** is 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 concepts and methods can be used to solve problems in the field. The **9th Edition** focuses on improved clarity and deeper understanding, and offers an embedded version of StatCrunch^{®} that enables students to analyze data sets while reading the book. A semester of differential and integral calculus is assumed as a prerequisite.

### Hallmark features of this title

**Mathematical support**gives engineers and scientists the proper context for statistical tools and methods.**Mathematical level**: Calculus is confined to elementary probability theory and probability distributions. Matrix algebra is used in coverage of linear regression material. Linear algebra and matrices are applied where treatment of linear regression and analysis of variance is covered.**Exercise sets**challenge students to solve problems in real scientific and engineering situations, many with**real data**from studies in bioengineering, business, etc.**Statistical software**coverage in case studies includes SAS® and MINITAB^{®}, with screenshots and graphics as appropriate.**Interaction plots**give examples of scientific interpretations and exercises using graphics.

### New and updated features of this title

**Revised text**focuses on improved clarity and deeper understanding rather than adding extraneous new material.**End-of-chapter material**strengthens the connections between chapters.- “
**Pot Holes**” comments remind students of the bigger picture and how each chapter fits into that picture. - These notes also discuss limitations of specific procedures and help students avoid pitfalls in misusing statistics.

- “
**Class projects**in several chapters provide the opportunity for students to gather their own experimental data and draw inferences from that data. These projects illustrate the meaning of a concept or provide empirical understanding of important statistical results, and are suitable for either group or individual work.**Case studies**provide deeper insight into the practicality of the concepts.

### Highlights of the DIGITAL UPDATE for MyLab Statistics

**Instructors**, contact your sales rep to ensure you have the most recent version of the course.

- Exercises in the MyLab are increased significantly, to
**45% coverage**of the textbook problems. **An embedded version of StatCrunch**^{®}in the accompany eTextbook allows students to analyze data sets while reading the book.

### Features of MyLab Statistics for the 9th Edition

#### Teach your course your way

**Enjoy flexibility.**Easily tailor your course to fit your needs. Create your own media and practice assignments, while managing sections and prerequisites.**Reach students early.**With Early Alerts, you'll get data, early on, identifying learners who may need extra support. Available with many courses.

#### Deliver trusted content

**Invigorate your course material.**Interactive features and course-specific resources bring concepts to life, fostering lasting comprehension.**Engage visual learners.**Educational videos, produced with authors and key contributors, help students visualize concepts and solve problems.

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**Personalize learning.**MyLab gives students the support they need to build confidence and improve results.**Offer on-the-spot guidance.**Immediate feedback on homework and quizzes helps learners quickly get back on track.

### 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
- Exercises
- 1.4 Measures of Variability
- Exercises
- 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
- Exercises

### 2. Probability

- 2.1 Sample Space
- 2.2 Events
- Exercises
- 2.3 Counting Sample Points
- Exercises
- 2.4 Probability of an Event
- 2.5 Additive Rules
- Exercises
- 2.6 Conditional Probability, Independence and Product Rules
- Exercises
- 2.7 Bayes' Rule
- Exercises
- 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
- Exercises
- 3.4 Joint Probability Distributions
- Exercises
- Review Exercises
- 3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

### 4. Mathematical Expectation

- 4.1 Mean of a Random Variable
- Exercises
- 4.2 Variance and Covariance of Random Variables
- Exercises
- 4.3 Means and Variances of Linear Combinations of Random Variables
- 4.4 Chebyshev's Theorem
- Exercises
- 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
- Exercises
- 5.3 Hypergeometric Distribution
- Exercises
- 5.4 Negative Binomial and Geometric Distributions
- 5.5 Poisson Distribution and the Poisson Process
- Exercises
- 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
- Exercises
- 6.5 Normal Approximation to the Binomial
- Exercises
- 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)
- Exercises
- 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
- Exercises

### 8. Sampling Distributions and More Graphical Tools

- 8.1 Random Sampling and Sampling Distributions
- 8.2 Some Important Statistics
- Exercises
- 8.3 Sampling Distributions
- 8.4 Sampling Distribution of Means and the Central Limit Theorem
- Exercises
- 8.5 Sampling Distribution of
*S*^{2} - 8.6
*t*-Distribution - 8.7
*F*-Distribution - 8.8 Quantile and Probability Plots
- Exercises
- 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
- Exercises
- 9.8 Two Samples: Estimating the Difference Between Two Means
- 9.9 Paired Observations
- Exercises
- 9.10 Single Sample: Estimating a Proportion
- 9.11 Two Samples: Estimating the Difference between Two Proportions
- Exercises
- 9.12 Single Sample: Estimating the Variance
- 9.13 Two Samples: Estimating the Ratio of Two Variances
- Exercises
- 9.14 Maximum Likelihood Estimation (Optional)
- Exercises
- 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 - Exercises
- 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
- Exercises
- 10.8 One Sample: Test on a Single Proportion
- 10.9 Two Samples: Tests on Two Proportions
- Exercises
- 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 Exercises 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
- Exercises
- 11.4 Properties of the Least Squares Estimators
- 11.5 Inferences Concerning the Regression Coefficients
- 11.6 Prediction
- Exercises
- 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
- Exercises
- 11.10 Data Plots and Transformations
- 11.11 Simple Linear Regression Case Study
- 11.12 Correlation
- Exercises
- 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
- Exercises
- 12.4 Properties of the Least Squares Estimators
- 12.5 Inferences in Multiple Linear Regression
- Exercises
- 12.6 Choice of a Fitted Model through Hypothesis Testing
- 12.7 Special Case of Orthogonality (Optional)
- Exercises
- 12.8 Categorical or Indicator Variables
- Exercises
- 12.9 Sequential Methods for Model Selection
- 12.10 Study of Residuals and Violation of Assumptions
- 12.11 Cross Validation,
*C*, and Other Criteria for Model Selection_{p} - Exercises
- 12.12 Special Nonlinear Models for Nonideal Conditions
- Exercises
- 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
- Exercises
- 13.5 Multiple Comparisons
- Exercises
- 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)
- Exercises
- 13.10 Random Effects Models
- 13.11 Case Study
- Exercises
- 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
- Exercises
- 14.4 Three-Factor Experiments
- Exercises
- 14.5 Factorial Experiments for Random Effects and Mixed Models
- Exercises
- Review Exercises
- 14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

### 15. 2^{k} Factorial Experiments and Fractions

^{k}

- 15.1 Introduction
- 15.2 The 2
Factorial: Calculation of Effects and Analysis of Variance^{k} - 15.3 Nonreplicated 2
Factorial Experiment^{k} - Exercises
- 15.4 Factorial Experiments in a Regression Setting
- 15.5 The Orthogonal Design
- Exercises
- 15.6 Fractional Factorial Experiments
- 15.7 Analysis of Fractional Factorial Experiments
- Exercises
- 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
- Exercises
- 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
- Exercises
- 16.3 Wilcoxon Rank-Sum Test
- 16.4 Kruskal-Wallis Test
- Exercises
- 16.5 Runs Test
- 16.6 Tolerance Limits
- 16.7 Rank Correlation Coefficient
- Exercises
- 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
- Exercises
- Bibliography

#### A. Statistical Tables and Proofs

#### B. Answers to Odd-Numbered Non-Review Exercises

#### Index

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