In my textbook for my statistics class, it says that $s^2$, sample variance is a "unbiased estimator" for population variance, $\sigma^2$. Does this mean that when we use $s^2$ as a point estimator for $\sigma^2$, it precisely equals $\sigma^2$? So $s^2$ is not even an estimation/approximation for $\sigma^2$? What does unbiased estimator mean?
Thank You!
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$\begingroup$$S^2$ is unbiased estimator for the population variance $\sigma^2$ because, as per definition
$$\mathbb{E}[S^2]=\sigma^2$$
there are other and most important properties of an estimator, i.e. consistency, sufficiency, efficiency, etc etc.
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