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The CLT holds for independent, identically distributed RVs. In the three-coin example the RVs are independent but not identically distributed: there are three d
by Schiphol 7y ago
The CLT holds for independent, identically distributed RVs. In the three-coin example the RVs are independent but not identically distributed: there are three distributions, one for each coin.
- bonoboTP 7y agoNo, it's the opposite: the 300 tosses are identically distributed, but they are not independent. They aren't independent because they all depend on a common cause: the choice of which coin to flip. Their property is also called "exchangeable" and it implies identical marginal distributions.
- Schiphol 7y agoRight, thanks. The averages are independent and not identically distributed, but that's irrelevant to the theorem, right?
- deleted 7y ago[deleted]