Re: Independent vs uncorrelated

dvsarwate@xxxxxxxxx wrote:

Jani Huhtanen asked:

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.

For the two-dimensional case, a proof is given in Chapter 6 of
Sheldon Ross's A First Course in Probability, Prentice-Hall.

We don't have that in our library. Could you outline the approach in the
prove?

--
Jani Huhtanen
Tampere University of Technology, Pori
.