You pick a card at random and with replacement twice from 3 cards numbered 1, 2, 3. Let S denote their sum and D the result of the first roll minus the second roll. Give the probability mass function of the product of S and D.

Name: You pick a card at random and with replacement twice from 3 cards numbered 1, 2, 3. Let S denote their sum and D the result of the first roll minus the second roll. Give the probability mass function of the product of S and D.
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The Answer is

\left( \begin{array} { c c c c c c c } 0 & - 3 & - 5 & - 8 & 3 & 5 & 8 \3 / 9 & 1 / 9 & 1 / 9 & 1 / 9 & 1 / 9 & 1 / 9 & 1 / 9\end{array} ight)

You Pick a Card at Random and with Replacement Twice