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Show an example of F(x,y) defined on [0,+∞)× [0, +∞) such that (i) F(0,0) = 0,...

Show an example of F(x,y) defined on [0,+∞)× [0, +∞) such that


(i) F(0,0) = 0,
(ii) F(+∞,+∞)=1

(iii) for every x ≥ 0, F (x, y) is increasing in y; for every y ≥ 0, F (x, y) is increasing in x,

(iv) and yet, F(x,y) is not a valid joint CDF function. That is, there is no random vector (X, Y ) whose joint CDF is F .

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