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This question already has an answer here:

If $X \sim \mathcal{N}(\mu,\sigma^2)$ where $\mu > 0$ and $\sigma > 2$, how do I find the PDF of $X^2$, and will it correspond to non-central Chi-square distribution?

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marked as duplicate by Xi'an, Peter Flom Apr 27 '18 at 10:52

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    $\begingroup$ Your questions are answered in the Wikipedia article. $\endgroup$ – whuber Apr 26 '18 at 22:59
  • $\begingroup$ Thanks for the quick comment but in article indicates unit variance, how does variance fit in the PDF $\endgroup$ – Ahmed Cheema Apr 26 '18 at 23:10
  • $\begingroup$ It merely establishes the units in which $X$ is measured and therefore is extremely easy to incorporate in all formulas. $\endgroup$ – whuber Apr 26 '18 at 23:22
  • $\begingroup$ @AhmedCheema make sure my edits were right. In particular the one with $\sigma > 2$. $\endgroup$ – Taylor Apr 27 '18 at 0:52