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I have found remembering that both the law of large numbers and the central limit theorem are dependent on the independent and identically distributed assumptio
by nyrikki 3y ago
I have found remembering that both the law of large numbers and the central limit theorem are dependent on the independent and identically distributed assumption.
As an example, many computing systems are Markovian, which is memoryless with an exponential distribution.
So the second part of I.I.D. doesn't hold. But may be close enough for your needs.
- mjb 3y agoHowever, in many real systems the aggregate behavior follows the asymptotic trend of the central limit theorem even though the underlying distributions may not fit the strict requirements.
- nyrikki 3y agoYes, I always start with the IID, but try watch for evidence that those assumptions need to change. Too many convenient properties are lost once you lose IID to prematurely drop it.