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Suppose $X$ is a random variable. Now, suppose I want to add a constant random variable to $X$. Should I denote the constant by a lower- or upper-case letter? So $X+A$ or $X+a$?

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    $\begingroup$ "Suppose $X$ is a normally distributed random variable." I am supposing, I am supposing, .... but what does normal-distribution have to do with this question? Do you think the answer might be different if $X$ were not a normally distributed random variable but some other kind of random variable, e.g. a $\chi^2$ random variable? $\endgroup$ – Dilip Sarwate Aug 2 '15 at 13:23
  • $\begingroup$ Sorry, it just happened to be case when I was thinking about this. I edited the question. $\endgroup$ – user83920 Aug 2 '15 at 15:32
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If you want to think of it as first and foremost a random variable (that happens to be constant), best to use $A$.

If you want to think of it primarily as a constant, it may be better to use $a$.

If in doubt, use $A$ but it can be (at least arguably) legitimate to use either.

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