In the central limit theorem, why does the population variance equal σ2/N, NOT σ2?

CFA Level I
#1

In the central limit theorem, why does the population variance equal σ2/N, NOT σ2?

#2

Where did you get this? Var(X) is σ2 while Var( X_bar) is σ2/n. I think population variance means Var(X), right? :upside_down_face:

#3

LOL. This is easier than we thought.
-From the population (whatever that distribution), with mean x̄ and variance σ2, we can get standard distributed samples as long as the sample size is greater than 30. OK this makes sense.
-So on, when you get samples, the size, mean, median are all different from the population, which makes the variance of samples different!!!

#4


This assumes each Xi is independent and identically distributed.

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