Probability and statistics courses are more popular than ever. Regardless of your major or your profession, you will most likely use concepts from probability and statistics often in your career.
The primary goal behind this book is offering the flexibility for instructors to build most undergraduate courses upon it. This book is designed for either a one-semester course in either introductory probability and statistics (not calculus-based) and/or a one-semester course in a calculus-based probability and statistics course.
The book focuses on engineering examples and applications, while also including social sciences and more examples. Depending on the chapter flows, a course can be tailored for students at all levels and background.
Over many years of teaching this course, the authors created problems based on real data, student projects, and labs. Students have suggested these enhance their experience and learning. The authors hope to share projects and labs with other instructors and students to make the course more interesting for both.
R is an excellent platform to use. This book uses R with real data sets. The labs can be used for group work, in class, or for self-directed study. These project labs have been class-tested for many years with good results and encourage students to apply the key concepts and use of technology to analyze and present results.
Author(s): Rodney X. Sturdivant, William P. Fox
Series: Textbooks in Mathematics
Publisher: CRC Press/Chapman & Hall
Year: 2022
Language: English
Pages: 428
City: Boca Raton
Cover
Half Title
Series
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
1 Introduction to Statistical Modeling and Models and R
1.1 What Is Modeling?
1.2 Overview and the Modeling Process
1.3 The Modeling Process
1.3.1 Mathematical Modeling
1.3.2 Models and Real-World Systems
1.3.3 Model Construction
1.4 Making Assumptions
1.5 Illustrative Modeling Examples
1.6 Technology
1.6.1 What Is R?
1.6.1.1 Introduction to R
1.6.2 The R Environment
1.6.3 R, Data, and Manipulating Data
1.6.3.1 Importing Data from EXCEL (as a csv file) to RStudio
1.7 Chapter 1 Exercises
1.8 Chapter 1 Projects
1.9 References and Additional Readings
2 Introduction to Data
2.1 Finding Basic Statistics
2.2 Chapter 2 Exercises
2.3 Displaying the Data
2.3.1 Data Ambiguity
2.3.2 Data Distortion
2.3.3 Data Distraction
2.3.4 Two Chart Types That Should Always Be Avoided
2.3.5 Good Graphical Displays
2.4 Chapter 2 Exercises
2.5 References and Suggested Readings
2.6 Good Displays of Categorical Data
2.6.1 Bar Charts
2.7 Chapter 2 Exercises
2.8 Displaying Quantitative Data
2.8.1 Symmetry
2.8.2 Stem and Leaf Plots
2.9 Chapter 2 Exercises
2.9.1 Displaying Quantitative Data with Histograms
2.10 Chapter 2 Exercises
2.11 Displaying Quantitative Data Using Boxplots and for Comparisons
2.11.1 Unequal Lengths
2.11.2 Comparisons
2.11.3 R (Retrieving Data) for Obtaining Displays
2.12 Chapter 2 Exercises
2.13 Summary: Displays of Data
2.13.1 Categorical Data Displays
2.13.2 Quantitative Displays
2.14 Chapter 2 Exercises
3 Statistical Measures
3.1 Measures of Central Tendency or Location
3.1.1 Describing the Data
3.1.2 The Mean
3.1.3 The Median
3.1.4 The Trimmed Mean
3.1.5 The Mode
3.2 Measures of Dispersion
3.2.1 The Variance and Standard Deviation
3.2.2 The Range and Interquartile Range (IQR)
3.3 Measures of Symmetry and Skewness
3.4 Summary with Descriptive Statistics Using R
3.4.1 Measures of Location
3.4.2 Measures of Spread
3.4.3 Measures of Symmetry and Skewness
3.5 Summary of Measures
3.5.1 Definition of “Skewness”
3.5.2 Definition of “Mean”
3.5.3 Statistics and Measures Summary
3.5.4 R (Retrieved Data and Descriptive Statistics)
3.6 Chapter 3 Exercises
4 Classical Probability
4.1 Introduction to Classical Probability
4.1.1 The Law of Large Numbers
4.2 Counting
4.2.1 The Multiplication Rule
4.2.2 Permutations and Combinations
4.2.3 Combinations
4.2.4 Computing Permutations and Combinations in R
4.3 Chapter 4 Exercises
4.4 Probability from Data
4.4.1 Intersections and Unions
4.4.2 The Addition Rule
4.4.3 Rule for Mutually Exclusive Sets
4.4.4 Addition Rule for Mutually Exclusive Events
4.4.5 Complement Rule
4.4.6 Conditional Probability
4.4.7 Independence
4.4.8 Definition of Independent Events
4.4.9 Mutually Exclusive and Independence
4.4.10 Review/Summary
4.4.11 Sampling and Experiments
4.4.12 Tree Diagrams
4.4.13 Review of Probability Laws
4.5 Chapter 4 Exercises
4.6 Bayes’ Theorem
4.6.1 Bayes’ Theorem
4.7 Chapter 4 Exercises
5 Discrete Distributions
5.1 Introduction to Discrete Random Variables and Distributions
5.2 Bernoulli Distribution
5.3 Binomial Distribution
5.4 Poisson Distribution
5.5 Chapter 5 Exercises
5.6 Other Discrete Distributions: Hypergeometric, Geometric, Negative Binomial
5.6.1 Hypergeometric Distribution
5.6.2 Geometric Distribution
5.6.3 Negative Binomial Distribution
5.7 Discrete Distribution Summary of Known Distributions
5.7.1 Binomial Distribution
5.7.2 Poisson Distribution
5.7.3 Geometric Distribution
5.7.4 Hypergeometric Distribution
5.7.5 Negative Binomial Distribution
5.8 Chapter 5 Exercises
5.9 Chebyshev’s Inequality
5.10 Chapter 5 Exercises
6 Continuous Probability Models
6.1 Introduction
6.2 Uniform Distribution
6.3 Exponential Distribution
6.3.1 Reliability
6.4 The Normal Distribution
6.5 Checking Normality
6.5.1 Inverse of Normal Distribution
6.6 Chapter 6 Exercises
7 Other Continuous Distribution (Some Calculus Required): Triangular, Unnamed, Beta, Gamma
7.1 Right Triangular Distribution
7.2 General Triangular Distributions
7.3 General Continuous Distributions
7.4 The Gamma Distribution
7.5 Beta Distribution
7.6 Chapter 7 Exercises
8 Sampling Distributions
8.1 The Sampling Distribution of the Mean
8.1.1 Sampling Distribution of the Mean of n = 49 from Skewed Distribution
8.2 Central Limit Theorem (CLT)
8.3 CLT Applications
8.4 Chapter 8 Exercises
9 Estimating Parameters
9.1 Confidence Interval for the Mean, Known Variance
9.2 Confidence Interval for the Mean, Unknown Variance
9.2.1 The Student’s t Distribution
9.2.2 Confidence Interval Using t Distribution, σ Not Known
9.3 Confidence Intervals for Proportions
9.3.1 Margin of Error and Sample Size
9.4 Confidence Intervals for a Population Variance and Standard Deviation
9.5 Chapter 9 Exercises
9.5.1 Find and Interpret the 95% and 99% CI for Problems 9.1–9.5
10 One Sample Hypothesis Testing
10.1 Introduction
10.2 Hypothesis Tests for a Population Mean; Large Samples (n ≥ 30) with σ Known
10.3 Hypothesis Tests for a Population Mean; σ Unknown
10.4 Hypothesis Tests for a Population Proportion
10.5 Hypothesis Tests and Inferences about a Population Variance
10.6 Chapter 10 Exercises
11 Inferences Based on Two Samples
11.1 Large Independent Samples (Both Sample Sizes m, n ≥ 30)
11.2 Large Independent Samples (Only One Sample Size Is ≥30)
11.3 Paired Data
11.4 Two Sample Tests on Proportions
11.5 Two Sample Tests on Variances
11.6 Chapter 11 Exercises
12 Reliability Modeling (Modified and Adapted from Military Reliability Modeling by Fox and Horton)
12.1 Introduction
12.2 Modeling Component Reliability
12.3 Modeling Series and Parallel Components
12.3.1 Modeling Series Systems
12.3.2 Modeling Parallel Systems (Two Components)
12.4 Modeling Active Redundant Systems
12.5 Modeling Standby Redundant Systems
12.6 Models of Large-Scale Systems
12.7 Summary of Reliability
12.8 References and Suggested Readings
12.9 Chapter 12 Exercises
13 Introduction to Regression Techniques
13.1 Correlation and Misconceptions
13.1.1 Correlation and Covariance
13.1.2 Correlation: A Measure of Linear Relationship
13.1.2.1 Correlation Is the Measure of Linear Relationship between Variables
13.1.2.2 Correlation: A Measure of Linear Relationship
13.1.3 Calculating the Correlation
13.1.4 Testing the Significance of a Correlation with Hypothesis Testing
13.2 Model Fitting and Least Squares
13.2.1 Coefficient of Determination, R-square
13.3 Curve-Fitting Criterion, Least Squares
13.4 Chapter 13 Exercises
13.5 Diagnostics and Their Interpretations
13.5.1 Coefficient of Determination: Statistical Term: R2
13.5.2 R2 = 1 − SSE/SST
13.5.3 Plotting the Residuals for a Least-Squares Fit
13.5.4 Percent Relative Error
13.6 Examples with Diagnostics and Inferential Statistics
13.6.1 Diagnostics
13.7 Polynomial Regression in R
13.8 Chapter 13 Exercises
13.9 Multiple Regression in R
13.9.1 Examples of Multiple Regression
13.10 Chapter 13 Exercises
14 Advanced Regression Models: Nonlinear, Sinusoidal, and Binary Logistics Regression Using R
14.1 Introduction
14.2 Review of Linear Regression
14.2.1 Correlation of Spring Data
14.2.2 Review of Linear Regression of Spring Data
14.3 Review of Polynomial Regression
14.3.1 Linear Regression of Hospital Recovery Data
14.4 Review of Quadratic (Polynomial) Regression of Hospital Recovery Data
14.4.1 Exponential Decay Modeling of Hospital Recovery Data
14.5 Sinusoidal Regression
14.5.1 Linear Regression of Shipping Data
14.5.2 Sinusoidal Regression of Shipping Data
14.5.3 Sinusoidal Regression of Afghanistan Casualties
14.6 Logistic Regression
14.6.1 A Binary Logistical Regression Analysis of Dehumanization
14.7 Conclusions and Summary
14.8 Chapter 14 Exercises
14.9 References and Suggested Reading
15 ANOVA in R
15.1 Introduction
15.1.1 When to Use a One-Way ANOVA
15.1.2 Assumptions of ANOVA
15.2 ANOVA Mechanics
15.2.1 One-Way ANOVA
15.2.2 Two-Way ANOVA
15.2.3 Two-Way ANOVA Calculation by Hand
15.3 ANOVA Using lm()
15.4 ANOVA Using aov()
15.5 References and Further Readings
15.6 Chapter 15 Exercises
16 Two-Way ANCOVA Using R
16.1 ANCOVA vs. Regression
16.2 Introduction to the ANCOVA Process by Example
16.2.1 Visualizing the Data
16.2.2 Independence
16.3 Fitting an ANCOVA
16.3.1 How Does R Know We Want to Carry Out ANCOVA?
16.4 Diagnostics
16.4.1 Normality Assumption
16.5 Interpreting the Results
16.6 Presenting the Results
16.7 Illustrious Example
16.8 Chapter 16 Exercises
16.9 References and Further Readings
Appendix A Labs/Projects
Lab 1 Descriptive Statistics and Displays
Lab 2 Probability and Distributions
Lab 3 Central Limit Theorem
The Letter r: Drawing Random Numbers
Producing a Vector of Sample Means
Lab 4 Hypothesis Testing
Lab 5 Regression in R
Lab 6 Reliability
Appendix B Answers to Selected Exercises
Chapter 2 Exercises
Chapter 3 Exercises
Chapter 4 Exercises
Chapter 5 Exercises
Chapter 6 Exercises
Chapter 7 Exercises
Chapter 8 Exercises
Chapter 9 Exercises
Chapter 10 Exercises
Chapter 11 Exercises
Chapter 12 Exercises
Chapter 13 Exercises
Chapter 14 Exercises
Chapter 15 Exercises
Chapter 16 Exercises
Index
