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What is the significance of the derivative of a probability density function of a continuous random variable ?

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    In short? None.2011-04-28
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    No more significance than derivatives of any other functions. For example, you might want to use the derivative to find out where the density has a maximum.2011-04-28
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    It's the instantaneous rate of change of probability density. 2011-08-26

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It reduces Lebesgue-stielgies integral to the usual Lebesgue integral in computing,which is easier.

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    +1 for [spelling Lebesgue correctly](http://math.stackexchange.com/questions/37990/mathematicians-whose-names-are-commonly-mispronounced), -1 for poor [Stieltjes](http://en.wikipedia.org/wiki/Lebesgue%E2%80%93Stieltjes_integration). :)2011-11-24