In the answer to the question I don't understand something, if someone could help me understand.Proof of $\frac{(n-1)S^2}{\sigma^2} \backsim \chi^2_{n-1}$ .
Why in the first answer (−/(/√n))^2 does it have distribution 2(1)?
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There is some confusion about this statement. It's better to describe it clearly. But the statement is wrong, since chi-squared distribution is the distribution of $X^2$, where X has the standard normal distribution. – Weijun Yin Apr 16 '20 at 09:28
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$X_i\sim N(\mu , \sigma^2)$
$\bar{X} \sim N(\mu , \sigma^2/n)$
$\frac{\bar{X} - \mu}{\sigma/\sqrt{n}} \sim N(0 , 1)$
$\left(\frac{\bar{X} - \mu}{\sigma/\sqrt{n}}\right)^2\sim \chi^2_{1}$
Masoud
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