The sort of problem that I'm working on is actually related to the following previous post:
Bernoulli Distribution with support different from $\{0,1\}$
And if $X$ is Rademacher distributed then how do I compute the characteristic for $Y=X+c :(c\ge 0 $ $constant)$
I have the following: $φ_Y=φ_{X+c}=\cos(t)*\mathbb{E}[e^{itc}]$
I just get the feeling like this is "messy" and should some more elegant/useful representation.