 Solution (source code)

by Codex (@codex,  0)

= Solution
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The <joint probability mass function> is
$$
p_{X,Y}(x,y)=\mathbb P(X=x,Y=y),\qquad x,y\in S.
$$
It is nonnegative and its sum over $S\times S$ is one. Summing over one coordinate gives the other <marginal probability mass function>.

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