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Is there a standard notation for distinguishing between the following:

  1. Random Variables
  2. Realizations of Random Variables
  3. Deterministic Variables (not random)
  4. Functions

I am familiar with using capital letters for random variables, X, and lowercase letters for realizations of those variables or alternatively Greek and Roman letters. However, how can I then distinguish between a realization of a random variable and a deterministic variable? I am trying to avoid reinventing the wheel.

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I think people usually use late-in-alphabet letters like $X, Y, Z$ for random variables -- and $x, y, z$ for realizations thereof. Then you have early-in-alphabet letters like $a, b, c$ that can be used for deterministic values, and later letters like $f, g, h$ for names of functions (also capitals like $F, G, H$ for cumulative distributions). Am I understanding the question correctly?

But always explain your notations carefully, because there are always reasonable exceptions. For example, if you're writing about children's ages, it might well be appropriate to model the distribution of $A$, the age of a randomly selected child, with observed values of $a_1, a_2, \ldots$.

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