Sorry,
the exact formula is V=(x-mu)' sigma^{-1}(y-mu).
However I have understand what you mean.
Thank you,
Paolo
"Herman Rubin" <[EMAIL PROTECTED]> ha scritto nel messaggio
92koov$[EMAIL PROTECTED]">news:92koov$[EMAIL PROTECTED]...
> In article <0OX26.738$[EMAIL PROTECTED]>,
> Paolo Covelli <[EMAIL PROTECTED]> wrote:
> >Hi,
>
> >let x, y be two i.i.d. N(mu, sigma) p_variate.
> >How can I show that the distribution of V=(x-mu)' sigma^{-1}(x-mu), where
> >sigma^{-1} is the inverse of co_variance matirx sigma, is symmetric?
>
> With the problem as stated, it does not have a
> symmetric distribution, as it is an unbounded
> positive random variable.
>
> However, I see no use of y in the expression.
> Change one of the x's in the formula for V to
> y, and it becomes symmetric, since both of the
> independent random variables (one is enough)
> x-mu and y-mu are symmetric.
> --
> 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, Dept. of Statistics, Purdue Univ., West Lafayette
IN47907-1399
> [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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