I'm having difficulties in thinking about the probability mass function (PMF) as a special case of the probability density function (PDF).

I understand that PMF's are used in discrete examples, but in the extreme, we could have a continuous distribution with small clusters or neighbourhoods around $\mathbb{Z}$ (to simulate the concentrated mass in a point in the discrete case) of infinite density.

Is the modelling of infinite density correct? Or should it be $0$ instead? Am I missing anything or doing anything wrong?

If you happen to have suggestions of viewing this problem in other ways, do suggest them.

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    $\begingroup$ Could you describe the actual problem that you are facing? What exactly do you want to model and how? What is the problem? $\endgroup$ – Tim Jan 29 at 14:50
  • $\begingroup$ @StubbornAtom your link seems to point to a linear algebra question that has nothing to do with this Q $\endgroup$ – Juho Kokkala Jan 31 at 18:12
  • $\begingroup$ @JuhoKokkala Dear god! I meant this one: math.stackexchange.com/questions/3095012/…. $\endgroup$ – StubbornAtom Jan 31 at 19:09
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    $\begingroup$ I'm voting to close this question as off-topic because it has been asked by the OP on math.SE as well (math.stackexchange.com/q/3095012/15941) where it has been answered already. $\endgroup$ – Dilip Sarwate Feb 3 at 14:22

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