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Suppose the bivariate cdf $F(a,b)=Pr(X\leq a, Y\leq b)$ is differentiable in $(a,b)$. Is it true that $\frac{\partial Pr(X\leq a, Y\leq b)}{\partial a}=Pr(X=a,Y\leq b)$?

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  • $\begingroup$ Would you need to ask this question if the "$,Y\le b$" references were dropped? If not, then consider how their appearance possibly could change the answer. $\endgroup$ – whuber Mar 2 '20 at 20:20
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    $\begingroup$ Thanks a lot. This makes it clear. $\endgroup$ – T34driver Mar 3 '20 at 0:38

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