# continuous

1. ### Independence of Bivariate Continuos RV's.

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.
2. ### testing for the change in correlation between 2 variables over a 3rd linear variable

I have a hypothesis that the strength of correlation between two continuous variables will decrease with higher levels of a third variable. To give an applied example of the problem, looking at the correlation between mothers weight and their adult child's weight, I expect the correlation to...