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Statistics: Continuous Methods

This lecture provides an introduction to the Central Limit Effect (CLE) and its significance in statistics. The CLE describes how the sum of a large number of independent random variables tends to follow a normal distribution, regardless of the original distributions of the variables. Key aspects covered include the properties of the normal distribution, specifically the empirical rule (68%, 95%, 99.7%) for standard deviations, and the challenge of summing random variables. A thorough grasp of the CLE is essential for statistical analysis and inference.

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Statistics: Continuous Methods

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  1. Statistics: Continuous Methods STAT 452/652 Fall 2008 Lecture 3: Central Limit Effect (slides only contain intro)

  2. Normal distribution

  3. Normal distribution

  4. Normal distribution 68% 95% 99.7%

  5. Central Limit Effect

  6. Summing random variables B A A+B

  7. Summing random variables A, B, C, D A+B A+B+C+D A+B+C

  8. Summing random variables Generally, summation changes the shape of the distribution: number of possible values, spread, mean, etc. There is no simple way to tell what is the distribution of A+B if we know A and B (that is, you HAVE to do some integration and stuff) ... and what about A+B+C+...+Z? We need a miracle to cope with this...

  9. Central Limit Effect A B

  10. Central Limit Effect 2 summands

  11. Central Limit Effect 3 summands

  12. Central Limit Effect 4 summands

  13. Central Limit Effect 5 summands

  14. Central Limit Effect 6 summands

  15. Central Limit Effect 7 summands

  16. Central Limit Effect 8 summands

  17. Central Limit Effect 9 summands

  18. Central Limit Effect 10 summands

  19. Central Limit Effect 20 summands

  20. Central Limit Effect 30 summands

  21. Central Limit Effect 40 summands

  22. Central Limit Effect 50 summands

  23. Central Limit Effect 100 summands

  24. Central Limit Effect 1000 summands Normal distribution

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