# 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.

#### BGM

##### TS Contributor
Yes your approach is correct, so what is your problem?

#### Actuarial_Deepika

##### New Member
I am unable to get the specified proof.

#### Dason

##### Ambassador to the humans
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.

#### Actuarial_Deepika

##### New Member
Thank you so much! You are a life saver!

#### 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.