Editing Full width at half maximum (section)

===Normal distribution===
{{see also|Gaussian beam#Beam waist}}

If the considered function is the density of a [[normal distribution]] of the form
<math display="block">f(x) = \frac{1}{\sigma \sqrt{2 \pi} } \exp \left[ -\frac{(x-x_0)^2}{2 \sigma^2} \right]</math>
where ''σ'' is the [[standard deviation]] and ''x''<sub>0</sub> is the [[expected value]], then the relationship between FWHM and the [[standard deviation]] is<ref>[http://mathworld.wolfram.com/GaussianFunction.html Gaussian Function – from Wolfram MathWorld<!-- Bot generated title -->]</ref>
<math display="block"> \mathrm{FWHM} =   2\sqrt{2 \ln 2 } \; \sigma \approx 2.355 \; \sigma.</math>
The FWHM does not depend on the expected value ''x''<sub>0</sub>; it is invariant under translations.
The area within this FWHM is approximately 76% of the total area under the function.