Alternate Proof of Correctness
Click to expandRecycling an identity for variance,
so
and by definition,
Note that, since x1, x2, · · ·, xn are a random sample from a distribution with variance σ2, it follows that for each i = 1, 2, . . ., n:
and also
This is a property of the variance of uncorrelated variables, arising from the Bienaymé formula. The required result is then obtained by substituting these two formulae:
Read more about this topic: Bessel's Correction
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