# source of proof for a characterization of normal distribution

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.

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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