Re: jointly gaussian

On 2006-08-29 15:27:01 -0300, unsettledinside@xxxxxxxxx said:

Thankyou very much for your answers..this newsgroup is incredibly high
quality and helpful!

What I understand by independence is just pdf(x,y) = pdf(x)pdf(y)

So
1. If one comes across a jointly normal distribution, one can be
assured that the individual variables are normally distributed.
2. The joint distribution of 2 independent normal variables will have
jointly normal distribution. However it is not necessary for them to be
independent to form a jointly normal distribution.

Correct?

OK. Jointly normal variables can be correlated.

Beware the situation in which you have some bivariate distribution and
you have know that both marginals are normal. So you have pdf(x,y)
and know that pdf(x) is normal and pdf(y) is normal. There is no guarantee
that pdf(x,y) is normal. To make it work you would have to know that
all the ax+by forms are normal for any and all a and b.

-b

Dilip V. Sarwate wrote:
<unsettledinside@xxxxxxxxx> wrote in message
news:1156868114.626734.60270@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

can a bivariate normal distribution be only made up of 2 random
variables with normal distribution (and independent of each other)?

Yes and No. Yes, if two random variables have a bivariate normal
distribution, then they are normal random variables. No, the two
variables do not need to be independent of each other, assuming that
when you say independence you mean stochastic independence.




In other words can two random variables with some distribution other than
normal give rise to a jointly normal distribution?

No.

Or is it just that for 2 normal variables to have a jointly normal
distribution, they need to be independent of aech other?

No, they don't have to be independent of each other in the usual
sense of independence in probability theory. Your harping on this
point leads me to suspect that you mean something else by the
phrase "independent of each other"


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