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
- 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 S2
- 8.6 t-Distribution
- 8.8 Quantile and Probability Plots
- Exercises
- Review Exercises
- 8.9 Potential Misconceptions and Hazards; Relationship to Mate
