What is a Marginal Distribution and How Does it Apply to F1(x)F2(y)?

[MathematicalPhysicist]

I'm not sure I understnad what is a marginal distribution, but i need to show that if F1,F2 are one dimensional cummulative distribution functions then I(x,y)=F1(x)F2(y) has F1 and F2 as its marginal distributions.

well if I(x,y)=P(X<=x,Y<=y) and if X and Y are independent, then it equals: P(X<=x)*P(Y<=y), then F1(x)=P(X<=x) F2(y)=P(Y<=y)
or in general: F1(x)=P(X<=x, Y$$\in$$A) F2(y)=P(X $$\in$$ B Y<=y) where A and B are intervals where the r.vs Y and X are defined.

but it's really a guess.

 

[EnumaElish]

What is the definition of a marginal distribution? How does that def. apply to F1(x)F2(y)?