A Basic Variance Question

I should know this from P, but I can't remember or find it on google:



Let's say we have a random variable, L*, which equals the sum of N identically distributed random variables L.



I've seen some questions where the Var(L*) = N*Var(L)

Yet, other questions where Var(L*) = Var(L)/N.



Is Var(L*) = Var(L)/N only when E(L) = 0? So there is less variance when the expected value is 0? Does it have to do with some nuance of the normal distribution I'm not following? :duh:

It seems like generally the variance of future loss questions are the times I see Var(L*) = Var(L)/N, but if it was EPV of death benefits for 100 people, it would be Var(Z*) = 100Var(Z)...

Can someone shed some light?

A Basic Variance Question