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QPD’s that meet Keelin and Powley’s definition have the following properties.
=== Probability density
Differentiating <math>x=F^{-1} (y)=\sum_{i=1}^n a_i g_i (y)</math> with respect to <math>y</math> yields <math>dx/dy</math>. The reciprocal of this quantity, <math>dy/dx</math>, is the [[probability density function]] (PDF)
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