Herman Rubin wrote:
> In article <[EMAIL PROTECTED]>,
> Charles Metz <[EMAIL PROTECTED]> wrote:
> >Guidi Chan wrote:
>
> > > A fair die is rolled 2 times. X1 and X2 is the # of
> > > points showing on 1st and 2nd rolls.
>
> > > U = X1 + X2; V = X1 - X2.
>
> > > Show that U and V are NOT independent.
> --snip--
> > > I'm basically stuck at trying to show that there not
> > > independent.
>
> >Try thinking about the mathematical definition of
> >"independence" and about the joint distribution of U and V.
>
> I suggest that, instead, you think about the intuitive
> meaning of independence, and how it is used. Objects
> are independent if information about some of them provides
> no information about probabilities of events from the
> others. It is easy to construct such situations, and
> even to see the dependence without computing.
With all due respect, Herman (and I mean that sincerely, because I
admire your regular contributions here), I would suggest that this may
be one situation where intuition isn't the best approach for most
neophytes, who tend to confuse independence and an absence of
correlation at the purely intuitive level.
Charles Metz
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