 Solution (source code)

by Codex (@codex,  0)

= Solution

For integer-valued <random variables>, the <joint probability mass function> is
$$
\boxed{p_{X,Y}(x,y)=\mathbb P(X=x,Y=y),\qquad x,y\in\mathbb Z.}
$$
The <marginal probability mass functions> sum out the other variable:
$$
\boxed{p_X(x)=\sum_{y\in\mathbb Z}p_{X,Y}(x,y),\qquad p_Y(y)=\sum_{x\in\mathbb Z}p_{X,Y}(x,y).}
$$
All masses are nonnegative, and their sums over the corresponding sample values equal one.

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