uppose
and
are two jointly normal random variables:
with correlation
.
We introduce two jointly normal variables
and
according to the
relationships


(Orthogonal normal variables)

and claim that
,
are iid
.
To verify such claim we
calculate
Similarly to the relationships
(
Orthogonal normal variables
) we
may represent any collection of jointly normal variables as a linear
combination of iid standard normal variables. We consequently treat the
jointly normal variables as vectors in the sense of elementary geometry:
In the above calculation, the
and
act as orthogonal basis and
acts like scalar product.
