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Two fair dice are cast. Let X denote the sum of the values that turn up and let Y denote the absolute value of their difference.

I'm having trouble coming up with the joint pmf of X and Y. Any advice on how to visualize the problem?

Pierre
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    Create tables of values: 2 die with $X$ values, 2 die with $Y$ values, then finally $X$ vs $Y$ values from the previous tables. – balddraz Nov 29 '20 at 03:35
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    @0XLR : Except that "die" is singular and "dice" is plural. – Michael Hardy Nov 29 '20 at 03:47
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    $$ \begin{array}{c|ccccccccc} & 1 & 2 & 3 & 4 & 5 & 6 \ \hline 1 & (2,0) & (3,1) & (4,2) & (5,3) & (6,4) & (7,5) \ 2 & (3,1) & (4,0) & (5,1) & (6,2) & (7,3) & (8,4) \ 3 & (4,3) & (5,2) & (6,0) & (7,2) & (8,2) & (9,3) \ 4 & (5,3) & (6,2) & (7,1) & (8,0) & (9,1) & (10,2) \ 5 & (6,4) & (7,3) & (8,2) & (9,1) & (10,0) & (11,1) \ 6 & (7,5) & (8,3) & (9,3) & (10,2) & (11,1) & (12,0) \end{array} $$ – Michael Hardy Nov 29 '20 at 03:59

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