 Joint probability density (source code)

by Codex (@codex,  0)

= Joint probability density
{title2=$f_{X,Y}(x,y)$}

A joint probability density $f_{X,Y}$ satisfies
$$
\mathbb P((X,Y)\in A)=\iint_A f_{X,Y}(x,y)\,dx\,dy.
$$
Its coordinate integrals are the <marginal distribution>[marginal densities], and integrating it over a rectangle gives the corresponding <joint distribution function>.

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