1 Definitions

• Key Concepts
• Levels of Measurement
• Measures of Central Tendency
• Measures of Dispersion
• Shapes of Distributions
• Univariate Statistics

2 Probability

• Axioms
• Probability Rules
  • Marginal Rule Explanation
  • Bayes’ Rule Explanation
  • Examples

3 Expectations

• Mean
• Variance
• Sample Mean and Variance
• Notation Clarifications
• Standard Deviation
• Covariance
• Correlation
• Autocorrelation
• Expectation Rules
  • Exercises
• Summary
• Appendix
  • Why Does Sample Variance Have n - 1 in the Denominator?

4 Probability Distributions

• Random Variables
  • Discrete Random Variables
  • Continuous Random Variables
• Permutations and Combinations
  • Permutations
  • Combinations
• The Binomial Distribution
  • Bernoulli Trial
  • Binomial Distribution
  • Mean and Variance
  • Shape
  • Examples
• The Normal Distribution
  • Properties
  • Applications
  • Rules
  • Examples
  • Approximating the Binomial Distribution
• The Poisson Distribution
  • Properties
  • Example
  • Approximating the Binomial Distribution

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Credits

• ChatGPT
• Sociology Graduate Statistics | University of Notre Dame
• STAT 414 Introduction to Probability Theory | Penn State
• H. Pishro-Nik, “Introduction to probability, statistics, and random processes”, available at https://www.probabilitycourse.com, Kappa Research LLC, 2014.
• EconMacro