Sum of independent non-normal random variables

Asked Jan 25 '14 at 22:43

Active Jan 25 '14 at 22:58

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I have a very simple question:

Can a sum of independent non-normal random variables be normal? (not approximately normal, or converging in distribution to a normal after some standardization)

I have been thinking about it and I couldn't find an example or a proof that rules out this possibility. This is not a homework problem -- it's just out of curiosity.

Thanks!

asked Jan 25 '14 at 22:43

Zhi Zhao

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Yes, I was thinking about independent random variables. Sorry. – Zhi Zhao Jan 25 '14 at 22:46
I've edited the question accordingly. – Zhi Zhao Jan 25 '14 at 22:47
Where is the original question? There is one speaking about joint normallity, not the same. – skan Oct 04 '16 at 09:13

Sum of independent non-normal random variables

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