Suppose (X_{n} sim chi_{n}^{2}), the chi-square with (n) degrees of freedom. Show that [frac{1}{sqrt{2 n}}left(X_{n}-n ight)

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Suppose \(X_{n} \sim \chi_{n}^{2}\), the chi-square with \(n\) degrees of freedom. Show that

\[\frac{1}{\sqrt{2 n}}\left(X_{n}-n\right) \rightarrow_{d} N(0,1)\]

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