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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 $\sum_{i=1}^{n} (Y_i - \mu)^2 \sim \chi^2_n$ .$\endgroup$
$\begingroup$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.$\endgroup$
self-study
tag and explain what is your difficulty with this standard result? It is covered and established in most Statistics textbooks. $\endgroup$