Independence of Bivariate Continuos RV's.

Actuarial_Deepika

New Member
By the two definitions of independence for bivariate continuous RVs: (1) F(x,y)=F_X(x)F_Y(y) and
(2) f(x,y)=f_X(x)f_Y(y).
Prove that these two are equivalent. That is: prove that (1) implies (2) and that (2) implies (1).

I tried to differentiate for one and integrate for the other.

Dason

I am unable to get the specified proof.
Yeah. We inferred that. The problem we're having is that you're literally giving us no information about what is giving you trouble.

Actuarial_Deepika

New Member
When I integrate it, what limits should i take?

BGM

TS Contributor
Actually just a few steps: following from the definition

$$F_{X,Y}(x, y) = \Pr\{X \leq x, Y \leq y\}$$

and almost finish the question.

BGM

TS Contributor
You are welcome. But I just wonder you do not have the definition in your textbook?

Actuarial_Deepika

New Member
Actually, I don't have the text book. I am trying to gather all the information off the internet.