= Joint probability mass function
{title2=$p_{X,Y}(x,y)=\mathbb P(X=x,Y=y)$}
For <discrete random variables> $X,Y$, their joint probability mass function assigns a <probability> to each possible ordered pair. Its entries are nonnegative and sum to one. <Marginalization> gives the <probability mass functions> $p_X(x)=\sum_y p_{X,Y}(x,y)$ and $p_Y(y)=\sum_x p_{X,Y}(x,y)$. In a table with rows indexed by $x$ and columns by $y$, these are the row and column totals. The <joint probability distribution> records how the coordinates occur together, while the <marginal distributions> describe each separately.
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