TITLE: What is the PMF and CDF of the difference between two discrete random variables?
QUESTION [0 upvotes]: I have found a lot of references for the continuous case but I can't seem to find much information about how to find the PMF and CDF of the difference for two discrete r.v. for which we know their CDF and PMF.

REPLY [0 votes]: If $X$ and $Y$ are two independent discrete random variables, the PMF of $Z=X-Y$ is the convolution of $X$ and $-Y$:
$$P(Z=z)=\displaystyle\sum_{k=-\infty}^{\infty}P(X=k)P(Y=z-k)$$
Source: https://stats.stackexchange.com/a/450958/40817
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