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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