Re: Statistical Indep and Corr of Normal RVs


Brenneman wrote:
This is from Wikipedia:

"It is sometimes mistakenly thought that one context in which
uncorrelatedness implies independence is when the random variables
involved are normally distributed.

Given what you cited from Wikipedia (about the joint normality),
I now believe your insertion of "(JOINTLY)" to my statement is correct,
even though I had thought it was not necessary.

B> I should understand this to mean:

B> "But ZERO correlation implies independence IF and ONLY
B> IF the random variables are (JOINTLY) Normal"

* But it is possible for two random variables X and Y to be so
distributed jointly that each one alone is normally distributed, and
they are uncorrelated, but they are not independent. Examples appear
below...."

Now I remember I had seen something related to this that I though
were "pathological" constructions that do not arise "in practice".

This last statement though seems to directly contradict yours (which I
will paraphrase a bit as):
"But ZERO correlation implies independence IF and ONLY IF the random
variables are Normal meaning each is a univariate Normal r.v."

Can you see the source of confusion?
Matt

Yes. It clearly contradicted mine, and I believe I was technically
incorrect in my statement. But there should be no confusion about it.
You had sorted out the difference between the theoretical constructs
and the practical situation. The joint normality requirement simply
makes it impossible to construct pathelogical counterexamples. :-)

Now everyone is happy, I think.

-- Reef Fish Bob.

.

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