Meaning of $p(X)$

I have recently come across the notation $$p(X)$$ i.e here. I have not seen this notation of mixing small $$p$$ and a random variable $$X$$ before. For instance lets assume we have a fair die such that $$p(x) = 1/6$$ for all $$x$$ in the sample space {1,2,3,4,5,6}. We draw a random variable $$X \sim p(x)$$. What would $$p(X)$$ denote in this case?

$$p$$ either denotes the PMF or PDF of a distribution. It is a non-random function.
When discussing entropy in the context of information theory, one often plugs in a random variable $$X$$ into its own PDF/PMF $$p$$, yielding a new random variable $$p(X)$$.
• @sn3jd3r Yes. ${}$ Apr 12, 2020 at 2:16