Re: Statistical Indep and Corr of Normal RVs

Reef Fish Bob,

Ok, I am going to test myself to see if I have this right.

When you say:
"But ZERO correlation implies independence IF and ONLY IF the random
variables are Normal",

I should understand this to mean:

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

and I see where now I got confused, as I was interpreting this to mean
that the _individual_ rvs had to have a normal distribution, which even
though it may be true, does not mean that the two rvs together are
jointly normal (as Charles Metz showed so clearly with that really nice
example). If the 2 rvs are jointly normal, then r=0 allows you to
separate their pdfs and establish independence. If you don't know their
joint pdf is normal, then the example (a la Charles Metz), shows you
can construct cases of 2 rvs which are not independent, yet have zero
correlation and marginal pdfs that are both normal.

Hopefully, this is correct ;>).

Thank you for your reply; I (think) I really understand something that
always puzzled me before.

Sincerely,
Matt Brenneman

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