# What is the physical meaning of the probability density function and cumulative distribution function?

I have started research in Electronic Engineering, where PDF & CDF take a core part in most of the applications. I have studied books on probability where they have discussed the PDF & CDF formulas and basic theory. But my objective is different, like thinking about their applications: e.g. If I take any graph like a unit step function graph (which have 3 piece-wise defined sub-functions -ve infinity to zero, at zero and zero +ve infinity) I should know about this that should I take/evaluate its conditional PDF or conditional CDF?

So generally I want to know the physical meaning of both conditional PDF & CDF in engineering applications? If anyone can explain this to me or recommend any literature on it that would be great.

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PDF: The closest physical concept I know is the actual density function, this is, a normalised function that tells you how the mass is distributed in a set o points, a line, a surface or a (hyper)volume of a body or set of bodies. CDF: This tells you about the mass cumulated in a certain region or set of points in the discrete case. Similarly, the expectation is related to the Centre of mass. –  user10525 Aug 1 '12 at 10:06