1) For the normal distribution it seems that the integral of the propability density function from [itex]\mu[/itex]-[itex]\sigma[/itex] to [itex]\mu[/itex]+[itex]\sigma[/itex] is independent of [itex]\sigma[/itex]. I guess that gives kind of a nice interpretation of [itex]\sigma[/itex]. But how do you prove this, when the antiderivative of an exponential with a square doesn't exist, and the limits are not from minus infinity to infinity?(adsbygoogle = window.adsbygoogle || []).push({});

2) Secondly it doesn't seem that for other distributions, their [itex]\sigma[/itex] has this neat property. So what on earth makes the standard deviation a useful number for these distributions?

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# Normal distribution, variance

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