## Sample variance calculation [closed]

Hi, I have quite a simple question but I can't for the life of me figure it out.

If you are given the sample variance as

$S^2 = \frac{1}{n-1}\sum\limits_{i=1}^{n}(X_i - \bar{X})^2$

How can you write the following?

$S^2 = \frac{1}{n-1}[\sum\limits_{i=1}^{n}(X_i - \mu)^2 - n(\mu - \bar{X})^2]$

All texts that cover this just skip the details but I can't work it out myself. I get stuck after expanding like so

$S^2 = \frac{1}{n-1}\sum\limits_{i=1}^{n}(X_i^2 -2X_i\bar{X} + \bar{X}^2)$

What am I missing?

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 This is probably more appropriate for mathstackexchange. I'm guessing it will be closed soon, so you might want to try asking it there. – John Engbers Jun 1 at 13:25