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## Statistics: Continuous Methods

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**Statistics: Continuous Methods**STAT 452/652 Fall 2008 Lecture 3: Central Limit Effect (slides only contain intro)**Normal distribution**68% 95% 99.7%**Summing random variables**B A A+B**Summing random variables**A, B, C, D A+B A+B+C+D A+B+C**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...**Central Limit Effect**2 summands**Central Limit Effect**3 summands**Central Limit Effect**4 summands**Central Limit Effect**5 summands**Central Limit Effect**6 summands**Central Limit Effect**7 summands**Central Limit Effect**8 summands**Central Limit Effect**9 summands**Central Limit Effect**10 summands**Central Limit Effect**20 summands**Central Limit Effect**30 summands**Central Limit Effect**40 summands**Central Limit Effect**50 summands**Central Limit Effect**100 summands**Central Limit Effect**1000 summands Normal distribution