I have read that "many" distributions converge to Gaussian distributions. The conditions mentioned along with are number of trials should be large enough and mean as well as variance should exist.

Is this equivalent to central limit theorem if we consider outcome of each trial following a distribution?

I want to know are these conditions sufficient?

If not what are the additional conditions?

What is the fundamental reason behind this?

Binomial and possion distributions follow this. Can I say binomial distribution is origin of each gaussian?

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