If I have a random sample $X_1^2, X_2^2, ... ,X_{100}^2$ with $X_i \sim N(0, \sigma^2)$, how can I find the two sided confidence interval for $\sigma^2$ based on my sample, using an $\alpha = 0.05$
2026-04-05 20:40:07.1775421607
Two-Sided confidence interval
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See http://www.kean.edu/~fosborne/bstat/06evar.html where it is described how the distribution of the variance estimator is related to a chi-squared distribution and they tell you the number of degrees of freedom for the chi-squared. (It's crucial to assume your original distribution is normal). To get confidence intervals for such a chi-squared distribution, you can e.g. see Wikipedia page on chi-squared distribution and get the CDF.