What is differential probability? [closed]

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I am trying to understand the following statement (taken from a context related to volumetric image rendering):

Density denotes the differential probability that a ray interacts with the volumetric “medium” of the scene at a particular point

What does differential probability mean? (especially that density in this context is defined at any point in 3D space)

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1 Answer

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If a distribution (here in 3D space) has a density $f(x,y,z)$, that means that for (almost) any volume in that space $V$, you can assign a probability to it by integrating the density (here "density" means probability per unit volume, very similar to, say, the concentration of salt in a solution):

$$P(V) = \int_V f(x,y,z)dV$$

From the above, you can see why it's also a "differential probability" (although I've never heard that term).

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