On Thu, 27 Jan 2000, Guidi Chan wrote:
> I've kinda hit a road block trying to figure out this question, it's a
> pretty basic question but it's been a while since I've taken a stats
> course so perhaps I could get some hints:
>
> 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.
What leads you to suppose that this is a _statistics_ question?
> This is what I have done so far: I've solved for the mean and
> variance of both U and V. I've found the covariance of U and V...which
> is cov(U,V) = var (X1) - var (X2).
Well, that tells you something. What relationship exists between var(X1)
and var(X2)? (But of course, this only tells you whether or not U and V
are correlated, not whether they are independent.)
> I'm basically stuck at trying to show that they're not independent.
> Any advice? Thanks in advance!
If you haven't picked up on the hints offered by Charles Metz and Herman
Rubin, you might try enumeration. The sample space is small enough for
this not to be prohibitive.
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