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5주차

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5주차

1. 1. Introduction to Probability and Statistics 5th Week (4/5) 1. Mathematical Expectations2. Special Probability Distributions
2. 2. Mathematical Expectations*: Definition- Discrete- Continuous *in Korean: 기대값
3. 3. Mathematical Expectations: Example
4. 4. Mathematical Expectations: Example
5. 5. Functions of Random Variables
6. 6. Functions of Random Variables
7. 7. Functions of Random Variables
8. 8. A Few Theorems on Expectation
9. 9. The Variance and Standard Deviation
10. 10. The Variance and Standard Deviation
11. 11. The Variance and Standard Deviation
12. 12. The Variance and Standard Deviation
13. 13. A Few Theorems on Variance
14. 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)”
15. 15. Standardized Random Variables
16. 16. Moments
17. 17. Moments
18. 18. Moment Generating Functions
19. 19. Some Theorems on Moment Generating Functions
20. 20. Characteristic Functions
21. 21. Some Theorems on Characteristic Functions
22. 22. Importance of Characteristic Functions
23. 23. Variance for Joint Distributions
24. 24. Covariance
25. 25. Some Theorems on Covariance
26. 26. Correlation Coefficient
27. 27. • Correlation coefficient ⇒ 양의 상관관계 ⇒ 음의 상관관계 ⇒ 무 상관관계
28. 28. Conditional Expectation, Variance, and Moments
29. 29. Understanding Conditional Probability FunctionWhen X=x, Conditional When Y=y, ConditionalProbability Function for Y Probability Function for X
30. 30. Chebyshev’s Inequality
31. 31. Law of Large Numbers
32. 32. Other Measures of Central Tendency
33. 33. Percentiles
34. 34. Other Measures of Dispersion
35. 35. Skewness
36. 36. Kurtosis