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Maybe that is correct. What I'm just missing is a simple "proof" or at least an idea of a proof why some assumptions are violated. In this case you could a gain
by MichaelRazum 7y ago
Maybe that is correct. What I'm just missing is a simple "proof" or at least an idea of a proof why some assumptions are violated. In this case you could a gain argue:
picking a coin random and then toss 300 times --> Multidimensional CLT. Not saying the article is wrong. I'm just saying, where should be a proof or at least a bit more evidence... Just a simple plot is not enough from my perspective
- Schiphol 7y agoThe 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]
- inimino 7y agoThe violated assumption is simply i.i.d. of the so-called "random variable", in this case the individual coin flips would need to be i.i.d. for the CLT to hold. Obviously that's not the case at all by construction of the experiment. So really, it would be extraordinary if the plot showed anything other than it does. While the explanation of why it doesn't apply was handwavy ("can't really be written as a sum in the same way as before"), it is certainly correct and the graph helps give the intuition.