joint density function,
n. (Statistics) a function of two or more random variables from which can be obtained a single probability that all the variables will jointly take specified values or fall in specified intervals. For example, given random variables X and Y on a space with probability P,
P[(X,Y) ∈ B] = ∫B f(x, y) dx dy
defines a joint probability on R2 with density f, with respect to Lebesgue measure; and for all Borel sets on the line
P(X ∈ B) = ∫B f(x) dx
where f(x) = ∫ f(x, y) dy.
P[(X,Y) ∈ B] = ∫B f(x, y) dx dy
defines a joint probability on R2 with density f, with respect to Lebesgue measure; and for all Borel sets on the line
P(X ∈ B) = ∫B f(x) dx
where f(x) = ∫ f(x, y) dy.