
Variance paradox
Hello guys, how are you?
Say we have to find Var(((a1)/a) x) which equals with ((a1)^2/a^2) Var (x)
But if we try Var(((a1)/a) x)= Var((1(1/a))x) =Var(x)+(1/(a^2))Var (x)
= (1+1/(a^2)) Var (x) is a different result from ((a1)^2/a^2) Var (x).
With an arithmetic example we see that the first way is correct but what is really going wrong with the second way? Thank you very much!

Re: Variance paradox
Hello,
The problem with the second one is that you get the sum of two random variables : X and (1/a)X.
But Var(X+Y)=Var(X)+Var(Y)+2cov(X,Y).
your formula will be okay if your two variables are independent (and hence cov(X,Y)=0), but obviously X and (1/a)X are not independent ;)

Re: Variance paradox
Oh thank you very much :))) You are correct! :)