Re: question about sample variance
The simple answer is that n-1 "works" to make it unbiased. The MLE estimator divides by n, but is biased. When you take the expectation of the MLE estimator, you see that dividing by n-1 instead of n makes the estimator unbiased. And people tend to like unbiased estimators. So it's not arbitrary, but there's not some particularly deep reasoning either.
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