I am studying Join probability distributions and random variables. I've come across joint distribution functions (or cumulative distribution functions), and the following property:
$F_X(x) = F_{XY}(x, \infty)$
I just want to make sure my understanding is correct. Does this mean to say that the marginal probability is equal to the joint probability where Y $P(Y=y)=1?$ What if the random variables X,Y are dependent?
Or does it mean to say that $F_X(X)$ is the same regardless of what Y is?
Can someone please explain this property to me?