If you make a scatterplot of all possible values of U and V you will
discover that for every value of U the mean value of V is 0. In other
words, the slope of the regression of U on V is zero. This, for me is proof
that U and V are independent.
Howard S Hoffman
Guidi Chan wrote:
> Hello,
>
> 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:
>
> Question:
>
> 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.
>
> > 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).
>
> I'm basically stuck at trying to show that there not independent.
>
> Any advice? Thanks in advance!
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