Hi,

I'm trying to show that the sample variance obtained from a random sampling without replacement is

$\displaystyle \frac{\sigma^2}{n}\left(1 - \frac{n - 1}{N - 1}\right) \quad

\mbox{where} \quad \sigma^2 = \frac{1}{N} \sum_i^N \left(x_i - \mu\right)^2 $

and \mu is the sample mean. A lot of books cite the factor $\displaystyle \left(1 - \frac{n - 1}{N - 1}\right) $ as a correction for small samples, but I couldn't derive it. Could someone help me here, please?