A pair of dice is thrown simultaneously. If X denotes the absolute difference of the numbers appearing on top of the dice, then find the probability…

X & $\displaystyle 0$ & $\displaystyle 1$ & $\displaystyle 2$ & $\displaystyle 3$ & $\displaystyle 4$ & $\displaystyle 5$ $\displaystyle \mathrm{P}(\mathrm{X})$ & $\displaystyle \frac{6}{36}=\frac{1}{6}$ & $\displaystyle \frac{10}{36}=\frac{5}{18}$ & $\displaystyle \frac{8}{36}=\frac{2}{9}$ & $\displaystyle \frac{6}{36}=\frac{1}{6}$ & $\displaystyle \frac{4}{36}=\frac{1}{9}$ & $\displaystyle \frac{2}{36}=\frac{1}{18}$