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If $Y_i$ (i=1,...,n) are iid N($\mu$,$\sigma^2$), how would I calculate the marginal pdf of the SSE?

On Wikipedia, I saw that $\sum$($Y_i$-$\bar{Y}$)$^2$ ~ $\sigma^2$$\chi$$^2$(n-1).

Any help would be appreciated!

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  • $\begingroup$ As far as I know, not very easily because of the fact that $\mu$ has to be estimated from the data. It might be worthwhile as a first step to try to show that $\sum_{i=1}^{n} (Y_i - \mu)^2 \sim \chi^2_n$ . $\endgroup$
    – dsaxton
    Commented Oct 4, 2016 at 3:37
  • $\begingroup$ Could you add the self-study tag and explain what is your difficulty with this standard result? It is covered and established in most Statistics textbooks. $\endgroup$
    – Xi'an
    Commented Oct 4, 2016 at 7:23
  • $\begingroup$ A proof of the above can be found here on the maths Stack Exchange. $\endgroup$
    – Xi'an
    Commented Oct 4, 2016 at 7:26

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