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I would like to derive the standard error of the variance for a sample taken from a Uniform distribution with bounds $a$ and $b$.

The standard error of the mean of that sample is straigtforward: $SE_{mean} = \frac{1}{\sqrt{3 n}} \frac{b-a}{2}$ where $n$ is the sample size.

If possible, I am also looking for the standard error of the standard deviation.

How can I proceed?

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