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From: Robert Israel on 19 Jun 2005 23:51
In article <d95e38$q90$1(a)nntp.itservices.ubc.ca>,
Robert Israel <israel(a)math.ubc.ca> wrote:
>In article <1119231980.397473.240530(a)g43g2000cwa.googlegroups.com>,
> <kentonyee(a)hotmail.com> wrote:
>>> >What are necessary and sufficient conditions to guarantee that Cov[X^2,
>>> >Y^2] = 0?
>>
>>> The definition: E[X^2 Y^2] - E[X^2] E[Y^2] = 0, or restatements thereof.
>>
>>i was thinking of a less tautological relationship, like
>>Cov[X^2, Y^2] = 0 if, and only if, X is "independent" of Y.
>>(But I'm not sure if "independence" is necessary or sufficient...)
>
>Sufficient, of course. But not at all necessary. Again, counterexamples
>are very easy to construct.

I should have said, assuming E[X^2] and E[Y^2] exist it's sufficient...

Robert Israel israel(a)math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada



From: Herman Rubin on 20 Jun 2005 17:53
In article <1119225653.199817.198360(a)g44g2000cwa.googlegroups.com>,
Kenneth T. Onyee <kentonyee(a)hotmail.com> wrote:
>Why does Cov[X,Y] = 0 insufficient to imply that
>Cov[ X^2, Y^2 ] = 0?

>What are necessary and sufficient conditions to guarantee that Cov[X^2,
>Y^2] = 0?

Cov[X^2,Y^2] = 0 is the only necessary and sufficient condition.

If X and Y are independent, which is the case for Cov[X,Y] = 0
for jointly normal random variables, then X^2 and Y^2 are
independent, which is sufficient for their covariance to vanish.


--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin(a)stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
From: didier salle on 27 Jun 2005 06:17
> Let X and Y be uncorrelated random variables.
> By construction, this means Cov[X,Y] = 0.
> Is there a simple expression for Var[XY]?
> Or for Cov[XY,X]?
>
> (I don't imagine that Var[XY] = Var[X] * Var[Y] +
> ???)
>
> Kenneth
>

Guys,

I'm also very interested in knowing the expression for var[XY], but as a function of var[X] and var[Y].

The expression you gave vs E(XY) ... is not very explicit to me.

Could you help me on this ??

Thanks in advance

didier
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