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How does the standard error work?

Let's say I have an unbiased estimator, which is the sample mean, to estimate $\theta$. When can you say that $$VAR[\overline{X}] = \frac{\sigma^2}{n} $$ ?

If so yes, if not: when is this true?

  • $\begingroup$ What does $\theta$ have to do with this question? Or do you mean $\sigma$? $\endgroup$ – Placidia Oct 29 '12 at 23:37
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    $\begingroup$ So long as you have an IID sample, this is always the variance of $\bar{X}$ (assuming the variance of each draw is $\sigma^2$). $\endgroup$ – assumednormal Oct 29 '12 at 23:52
  • $\begingroup$ Ah, I saw this onlinecourses.science.psu.edu/stat414/node/167 I understand it completely now :) $\endgroup$ – Applied mathematician Oct 30 '12 at 0:03

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