3 ms·
"Central Limit Theorem" says that "adding (bounded variance) stuff together makes it converge to a Gaussian" (roughly). On the other hand, when you are adding r
by fjkdlsjflkds 4y ago
"Central Limit Theorem" says that "adding (bounded variance) stuff together makes it converge to a Gaussian" (roughly). On the other hand, when you are adding random variable together, you are actually convolving their densities. Thus, what the CLT says is that a gaussian is some sort of attractor/fixed point of the "dynamic process" of convolving (finite energy/bounded variance) distributions.
- amitport 4y agoThanks! Besides bounded variance they should also generally be independent. Or at least I'm not aware of a dependent variable version.
- fjkdlsjflkds 4y agoThere are (several) central limit theorems for dependent variables, but you often have to assume other things as well (e.g., stationarity, bounded third moment, and/or limited-range correlations) for it to work. Example: https://link.springer.com/chapter/10.1007/978-1-4612-0865-5_9 https://link.springer.com/chapter/10.1007/978-1-4612-0865-5_...