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.
In article <[EMAIL PROTECTED]>,
Howard S. Hoffman <[EMAIL PROTECTED]> wrote:
>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.
For U and V to be independent, it is not enough that the mean of V
conditional on any particular value for U is always the same. It must
be that the conditional distribution for V given any particular value
for U is always the same. It is quite possible for the mean to be the
same while the conditional distribution is different in other ways,
eg, the standard deviation might be different.
Radford Neal
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