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Day 6: The Central Limit Theorem I
Day 6: The Central Limit Theorem I
Central Limit Theorem
The central limit theorem (CLT) states that, for a large enough sample (), the distribution of the sample mean will approach normal distribution. This holds for a sample of independent random variables from any distribution with a finite standard deviation.
Let be a random data set of size , that is, a sequence of independent and identically distributed random variables drawn from distributions of expected values given by and finite variances given by . The sample average is:
For large , the distribution of sample sums is close to normal distribution where: