None of those things matter to the central limit theorem.
If I have IID observations with finite 2nd moment (variance), then their average will pretty quickly converge to a Gaussian distribution. And I can relax a lot of this and still recover a variant of CLT.
Of course maybe the calculation is different, eg it’s not like there are N independent observations, but rather some other complex condition solved for the mean estimate.
If I have IID observations with finite 2nd moment (variance), then their average will pretty quickly converge to a Gaussian distribution. And I can relax a lot of this and still recover a variant of CLT.
Of course maybe the calculation is different, eg it’s not like there are N independent observations, but rather some other complex condition solved for the mean estimate.