# How come that $Var(sX)=s^2Var(X)$ but for $s$ random variables with equal distribution $Var(\sum_{i=1}^s X_i)=sVar(X)$


Thank you.

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Your second statement is only true if the variables are uncorrelated. In your first statement, the summed variables are maximally correlated: they're all equal. –  Chris Eagle Oct 25 '12 at 16:18
Take $s=2$. $$\text{var}(sX) = \text{var}(X+X) = \text{var}(X)+\text{var}(X)+2\text{cov}(X,X) = 4\text{var}(X)=s^2\text{var}(X)$$ –  Dilip Sarwate Oct 25 '12 at 16:19
@ChrisEagle: Thanks, I meant to write it. –  Ben Benli Oct 25 '12 at 16:21
In general, for independent $A$ and $B$, we have $\Var(aA+bB)=a^2\Var(A)+b^2\Var(B)$.