Gaussian Idendity

**asingh88** · March 10th 2010, 08:29 AM

Can anyone help me on this

**CaptainBlack** · March 10th 2010, 10:13 AM

Originally Posted by asingh88

Can anyone help me on this

You need to evaluate:

$I = \int_{-\infty}^{\infty} x^2\ \frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{x^2}{x\sigma^2}}\; dx$

You can do this by parts spliting the integral, and integrating by parts:

$I = \int_{-\infty}^{\infty} [x]\ \left[\frac{x}{\sqrt{2\pi}\sigma}e^{-\frac{x^2}{x\sigma^2}}\right]\; dx$

CB

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