Sum and difference modulo \(m\) between two independent random variables (Q1204487)

The author defines sum and difference modulo \(m\) for two independent discrete random variables, which attain values \(0,1,\dots,m-1\) with probabilities \(p_ 0,p_ 1,\dots,p_{m-1}\) and \(q_ 0,q_ 1,\dots,q_{m-1}\), resp. \((\sum_ i p_ i=\sum_ i q_ i=1)\). For both the quantities, the distribution, expected value and variance are derived. The case when one of the components is distributed uniformly is also examined.