= Product of finite probability distributions
{title2=$p(x,y)=p_1(x)p_2(y)$}
Given two <finite probability distributions>, assign the product of their <probability masses> to each <ordered pair>. The support is the <Cartesian product> of the two positive-mass supports. Distributivity gives $\sum_{x,y}p_1(x)p_2(y)=(\sum_xp_1(x))(\sum_yp_2(y))=1$. This is the joint distribution for independent coordinate outcomes; it is a construction from the marginals, not a claim that arbitrary jointly observed coordinates are independent.
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