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 $X+a$?
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.