If the r.v. X has N(mu,sigma^2) then the distribution of Z=(fracX-musigma)^2 is:

Q58Section III (Statistics)58 of 84

The square of a standard normal is $\chi^2_1$

If the r.v. X has $N(\mu,\sigma^2)$ then the distribution of $Z=\bigl(\frac{X-\mu}\sigma\bigr)^2$ is:

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