Probability and Statistics

Index

• 1. Foundations and Combinatorics
  • 1.1 Data, Populations, and Variables
  • 1.2 Set Theory for Probability
  • 1.3 Counting Principles
• 2. Descriptive Statistics
  • 2.1 Organizing Data
  • 2.2 Measures of Center
  • 2.3 Measures of Spread
  • 2.4 Position and Shape
  • 2.5 Bivariate Description
• 3. Probability Theory
  • 3.1 Sample Spaces and Events
  • 3.2 Axioms and Basic Rules
  • 3.3 Conditional Probability and Independence
  • 3.4 Bayes' Theorem
  • 3.5 Measure-Theoretic Foundations
• 4. Random Variables and Distributions
  • 4.1 Discrete Random Variables
  • 4.2 Continuous Random Variables
  • 4.3 Expectation and Moments
  • 4.4 Transformations of Random Variables
• 5. Common Probability Distributions
  • 5.1 Discrete Distributions
  • 5.2 Continuous Distributions
  • 5.3 The Normal Distribution
  • 5.4 Sampling Distributions Families
  • 5.5 Stochastic Processes Preview
• 6. Multivariate Probability
  • 6.1 Joint Distributions
  • 6.2 Conditional Distributions
  • 6.3 Dependence and Covariance
  • 6.4 Sums and Multivariate Models
  • 6.5 Inequalities and Limit Theorems
• 7. Sampling and Study Design
  • 7.1 Sampling Methods
  • 7.2 Experimental Design
  • 7.3 Sampling Distributions
  • 7.4 Bias and Data Quality
• 8. Statistical Estimation
  • 8.1 Point Estimation
  • 8.2 Estimation Methods
  • 8.3 Confidence Intervals
  • 8.4 Resampling Methods
• 9. Hypothesis Testing
  • 9.1 Framework of Testing
  • 9.2 Tests for Means and Proportions
  • 9.3 Categorical Data Analysis
  • 9.4 Analysis of Variance
  • 9.5 Nonparametric Tests
  • 9.6 Theory and Practice of Testing
• 10. Regression and Predictive Modeling
  • 10.1 Simple Linear Regression
  • 10.2 Multiple Regression
  • 10.3 Assumptions and Diagnostics
  • 10.4 Model Selection and Regularization
  • 10.5 Generalized Linear Models
• 11. Bayesian Statistics
  • 11.1 Bayesian Framework
  • 11.2 Bayesian Inference
  • 11.3 Computational Bayesian Methods
• 12. Advanced and Applied Topics
  • 12.1 Time Series Analysis
  • 12.2 Multivariate Statistical Methods
  • 12.3 Survival and Reliability Analysis
  • 12.4 Causal Inference
  • 12.5 Statistical Learning and Decision Theory
  • 12.6 Communicating Statistical Results

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