Question $15$

A red die and a blue die are thrown. Let $S$ be a random varlable that denotes the square of the difference between the two numbers on the dice. For example, if the red die comes up $2$ and the blue die comes up $5,$ then $S=(2-5{)}^2=9.$ What is the distribution over S$?$

$(0,\frac{1}{6}),(1,\frac{5}{18}),(4,\frac{4}{18}),(9,\frac{3}{18}),(16,\frac{2}{18}),(25,\frac{1}{18})$

$(0,\frac{5}{36}),(1,\frac{5}{18}),(4,\frac{4}{18}),(9,\frac{3}{18}),(16,\frac{2}{18}),(25,\frac{1}{18})$

$(0,\frac{5}{36}),(1,\frac{4}{18}),(4,\frac{3}{18}),(9,\frac{2}{18}),(16,\frac{1}{18}),(25,\frac{1}{18})$

$(1,\frac{4}{18}),(4,\frac{5}{18}),(9,\frac{4}{18}),(16,\frac{3}{18}),(25,\frac{2}{18})$