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?


1 Answer 1


$p$ either denotes the PMF or PDF of a distribution. It is a non-random function.

You can plug a random variable into a function to get a new random variable.

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 $p(X)$.

  • $\begingroup$ So for the example in the questions p(X) is a random variable but the outcome is 1/6 always? $\endgroup$
    – sn3jd3r
    Apr 12, 2020 at 2:13
  • $\begingroup$ @sn3jd3r Yes. ${}$ $\endgroup$
    – angryavian
    Apr 12, 2020 at 2:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.