Probability and Statistics for Engineers and Scientists

Preface

 

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 127

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 S2

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

            Exercises

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, Cp, and Other Criteria for Model Selection

            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. 2k Factorial Experiments and Fractions

15.1 Introduction

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

15.3 Nonreplicated 2k Factorial Experiment

            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