prove the rectangle inequality for joint cdfs

prove the rectangle inequality for joint cdfs

Let F(x,y) be a bivariate CDF (i.e., the joint CDF of two r.v.s). Prove that for all a1 <= b1 and a2 <= b2,

F (b1 , b2 ) – F (a1 , b2 ) – F (b1 , a2 ) + F (a1 , a2 ) >=0 

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