tony873004

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homework question:

Show by numerical calculation that, for the Gaussian probability distribution, the full-width at half maximum [tex]\Gamma[/tex] is related to the standard deviation by [tex]\Gamma=2.354 \sigma[/tex].

What is a numerical calculation? Does this just mean "do the math", or does it mean numerical as in numerical vs. analytic methods, where I'm supposed to make the computer crunch a whole bunch of otherwise-unmanagable numbers to get an answer?

Any idea how to do this problem? I know that the standard deviation is equal to the square root of the mean. And I know that the full-width, half max is equal to the width of the curve halfway to the top of the curve. But I don't see a formula for computing it. When describing it, the book gives [tex]p_G \left( {\mu \pm 1/2\Gamma ,\mu ,\sigma } \right) = 1/2p_G \left( {\mu ;\mu ,\sigma } \right)[/tex]

There's a nice graph in the book showing standard deviation and FWHM, where eye-balling it, 2.354 seems like reasonable number.

**1. Homework Statement**

**2. Homework Equations**

**3. The Attempt at a Solution**