Let $x$ be a constant in $\mathbb{R}$.
Let $y$ be a random number that is generated according to a certain probability distribution.
I want to make the sum
$$x + y$$
However, I am not sure how to make it clear that $y$ is a random number (without using the English sentence that tells the reader that it is a random number).
I tried to write
$$x + y, y \sim f$$
where $f$ is the PDF or the PMF of the random variable associated with $y$.
However, here $y$ is the realization of the underlying random variable, not the random variable itself, so writing $y \sim f$ is abuse of notation.
Should I write something like
$$x + y, Y \sim f(y)$$
instead? However, now I have to make clear the connection between $Y$ (the RV) and $y$ (its realization), and how would I go about doing that using a concise mathematical notation?
Can anyone help?
In the context of probability, it is customary to use capitalized, italicized letters - generally X and Y - to denote random variables.
Discrete Random Variables