This is rather indirect, but I felt like answering this with inequalities, using a thread you were on earlier this year.Summary: Marginal distributions for multivariable
Let F(x,y) be the joint distribution for random variables X and Y (not necessarily independent). Is ##lim_{y\to \infty}F(x,y)## the distribution function for X? I believe it is. How to prove it?
##F_X(x) + F_Y(y) - 1 \leq F_{X,Y}(x,y) ## |