If X1, X2, Xn are iids, this means that:

Var(X1+X2+...+Xn) = Var(X1) + Var(X2) +...+Var(Xn), right??

but does : Var(X1^2 + X2^2 + ... + Xn^2) = Var(X1^2) + Var(X2^2)+...+Var(Xn^2)?

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- Aug 17th 2011, 12:42 AMfallingleaves75If X1, X2, ...., Xn are iid does that necessarily mean X1^2, X2^2, ..., Xn^2 are iids
If X1, X2, Xn are iids, this means that:

Var(X1+X2+...+Xn) = Var(X1) + Var(X2) +...+Var(Xn), right??

but does : Var(X1^2 + X2^2 + ... + Xn^2) = Var(X1^2) + Var(X2^2)+...+Var(Xn^2)? - Aug 17th 2011, 01:57 AMgirdavRe: If X1, X2, ...., Xn are iid does that necessarily mean X1^2, X2^2, ..., Xn^2 are
If are independent then so are . To see that, take and let . We have

and since are independent, we have and we are done.

We conclude that your formula is true if exists (but the problem doesn't come from the independence).