Re: Independent vs uncorrelated

Jani Huhtanen wrote:

Ben wrote:

Could someone clarify the diff between independent and uncorrelated
random variables?

Partho

Any spherically symmetric joint distribution implies uncorrelatedness.
However, gaussian joint distribution is the _only_ distribution that may
be both spherically symmetric (i.e., uncorrelated) and can be expressed as
product:

P(X0,X1,...,Xn)=P(X0)P(X1)...P(Xn).


BTW. Does anyone know a proof that the only joint distribution that can be
both spherically symmetric and such that the corresponding RVs are
independent is gaussian distribution? Or equivalently proof for that the
only separable spherically symmetric 2d (or kd) kernel is gaussian.

--
Jani Huhtanen
Tampere University of Technology, Pori
.