A joint distribution encodes the dependencies between its two marginal distributions (here in the simple case of a density with respect to a product of measures). en.wikipedia.org/wiki/Marginal_…
Fun (...) fact: the figure was generated backwards: from fX and fY, the joint distribution f is computed as the solution of an entropic regularized Optimal Transport (aka Schrodinger's problem).
A much simpler approach (but less pleasing visually) would be to take f(x,y)=fX(x)fY(y) (corresponding to the limit of infinite entropic regularization, ie infinite temperature of the gaz for Schrodinger, or independent random variables for probabilists).
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