:

It's well known that has a distribution with degrees of freedom. It's also well known that the variance of a distribution with degrees of freedom is . Therefore:

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An approach similar to the one used below can also be used but it's more tedious.

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:

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I'll cheat and get the moments and from here: http://en.wikipedia.org/wiki/Normal_distribution (the other moments were shown in my reply to your previous unbiased estimator question)

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Therefore .

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Therefore .