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It is well known that under normality assumption, the sample mean and sample variance are independent, by Basu's Theorem. My question is that, is the normal distribution the only distribution whose sample mean is independent of sample variance? Thanks!

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    $\begingroup$ The answer for the independence of sampling distributions is "yes". Otherwise, for population distributions, a number of them have independent mean and variance. See stats.stackexchange.com/questions/4354/…. This is possibly a duplicate question. $\endgroup$ – dnqxt Apr 20 at 1:52

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