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i am reviewing how to prove the variance of a Gaussian, and I am stuck very early on, following the proof at this link:[first two lines of variance proof

On the second line, after this substitution, where did the $\sqrt2\sigma$ come from on the constant outside of the integral?

Scott
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    Hi: They are using the substitution $t = \frac{x - \mu}{\sqrt{2} \sigma} $. So, when they calculate $dt$, it ends up being $\frac{1}{\sqrt{2}\sigma} dx$. So, thats why it ends up in the numerator on the second line. – mlofton Sep 12 '22 at 20:02
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    The first line of my post at https://stats.stackexchange.com/a/415436/919 answers this. Some intuition is given at https://stats.stackexchange.com/a/49794/919. Ultimately, this is purely a Calculus question. – whuber Sep 12 '22 at 20:16
  • @mlofton thank you! – Scott Sep 12 '22 at 20:25
  • I'm glad to help. Usually, I'm getting help !!!!! – mlofton Sep 14 '22 at 05:22

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