Given $X_1...X_n\stackrel{iid}{\sim} N(\mu,\sigma^2)$ and $U=\sum_{i=1}^n (X_i-\overline{X})^2$, why is $U\sim\sigma^2 \chi_{n-1}^2$ ?
And what would be the distribution of $V=\sum_{i=1}^n (X_i-\mu)^2$ ?
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Sign up to join this communityGiven $X_1...X_n\stackrel{iid}{\sim} N(\mu,\sigma^2)$ and $U=\sum_{i=1}^n (X_i-\overline{X})^2$, why is $U\sim\sigma^2 \chi_{n-1}^2$ ?
And what would be the distribution of $V=\sum_{i=1}^n (X_i-\mu)^2$ ?