What is the Central Limit Theorem? Explain it. Why is it important?

What is the Central Limit Theorem? Explain it. Why is it important?



The CLT states that the arithmetic mean of a sufficiently large number of iterates of independent random variables will be approximately normally distributed regardless of the underlying distribution. i.e: the sampling distribution of the sample mean is normally distributed.
- Used in hypothesis testing
- Used for confidence intervals
- Random variables must be iid: independent and identically distributed
- Finite variance

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