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I want to know the proof of the following statement about normal distribution:

If the sample mean and sample variance are independent for a population, then the distribution of the population is normal.

I cannot find the proof in any probability/statistics textbook that I have. Please help.

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Where did you see the assertion that this is true? Did the assertion say the population is normal if this is true of all sample sizes? – Michael Hardy Feb 20 '12 at 19:54
@Michael Hardy: Yes, I think independence is true for all sample sizes in order to get the assertion. I forgot where I see this assertion. – littleEinstein Feb 20 '12 at 19:55

See this question on Stats.SE

There are articles quoted here but no proofs shown. Wikipedia also quotes an article.

So far I haven't found the proof

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I see. Not sure if any textbook contains the proof, besides the two papers referenced therein. – littleEinstein Feb 20 '12 at 20:59

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