1. ## Simple Covariance Theory

In this problem, there is a given f(x) (continuous case)
and they say that U=X and v=X²
the first question is
a)find that Cov(U,V) = 0 which is easily done
then,
b)show that U and V are DEPENDANT.

Now I know that if U and V and independant, Cov(U,V) = 0
although the converse is not true.
But now, how do I show that U and V are dependant?

2. Originally Posted by suissa
In this problem, there is a given f(x) (continuous case)
and they say that U=X and v=X²
the first question is
a)find that Cov(U,V) = 0 which is easily done
then,
b)show that U and V are DEPENDANT.

Now I know that if U and V and independant, Cov(U,V) = 0
although the converse is not true.
But now, how do I show that U and V are dependant?
p(u,v)=q(u)r(v)

RonL

3. But what is q and what is r?
and i assume p(u,v) means probability of u and v?

Thanks.

4. Originally Posted by suissa
But what is q and what is r?
and i assume p(u,v) means probability of u and v?

Thanks.
They are the densities of the marginal distributions of u and v.

RonL

5. Ahhhh
You use marginals to show it!
Smart.
Thanks a lot.