<s>[INST] To estimate the mean of a population, we use the sample mean \(\bar{X}\) as an unbiased estimator. An unbiased estimator is a statistic that has an expected value \(E(\hat{\theta})\) equal to its parameter \(\theta\), where \(\hat{\theta}\) represents the estimator of \(\theta\). For estimating the variance of a population, we have two choices, \(S^2 = \sum_{i=1}^{n} \frac{(X_i - \bar{X})^2}{n}\) and \(S^2 = \sum_{i=1}^{n} \frac{(X_i - \bar{X})^2}{n-1}\). Which one of these is an unbiased estimator of the population variance \(\sigma^2\)?[/INST]