5주차
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The document is an introduction to probability and statistics that covers topics like mathematical expectations, special probability distributions, functions of random variables, variance, standardized random variables, moments, moment generating functions, characteristic functions, covariance, correlation coefficients, conditional expectations, and other statistical concepts in the fifth week of the course.
5주차
- 1. Introduction to Probability and Statistics 5th Week (4/5) 1. Mathematical Expectations 2. Special Probability Distributions
- 2. Mathematical Expectations*: Definition - Discrete - Continuous *in Korean: 기대값
- 5. Functions of Random Variables
- 6. Functions of Random Variables
- 7. Functions of Random Variables
- 8. A Few Theorems on Expectation
- 9. The Variance and Standard Deviation
- 10. The Variance and Standard Deviation
- 11. The Variance and Standard Deviation
- 12. The Variance and Standard Deviation
- 13. A Few Theorems on Variance
- 14. Compare! Vs. is true for any random variables is true for only independent variables is true for only independent variables Not “Var(X) – Var(Y)”
- 16. Moments
- 17. Moments
- 19. Some Theorems on Moment Generating Functions
- 21. Some Theorems on Characteristic Functions
- 22. Importance of Characteristic Functions
- 23. Variance for Joint Distributions
- 24. Covariance
- 25. Some Theorems on Covariance
- 27. • Correlation coefficient ⇒ 양의 상관관계 ⇒ 음의 상관관계 ⇒ 무 상관관계
- 28. Conditional Expectation, Variance, and Moments
- 29. Understanding Conditional Probability Function When X=x, Conditional When Y=y, Conditional Probability Function for Y Probability Function for X
- 31. Law of Large Numbers
- 32. Other Measures of Central Tendency
- 33. Percentiles
- 34. Other Measures of Dispersion
- 35. Skewness
- 36. Kurtosis