Suppose we roll two dice and let X and Y be the two numbers

Suppose we roll two dice and let X and Y be the two numbers that appear. Find the distribution of |X - Y|.

Solution

If two dice rolled, then total number of outcomes are 6*6 =36

(X-Y| takes values 0,1,2,3,4,5

(X-Y| takes value 0 when the events are (1,1),(2,2), (3,3),(4,4),(5,5),(6,6)

Therefore P((X-Y|=0) =6/36

Similarly (X-Y| takes value1 when the events are (1,2),(2,1), (3,2),(2,3),(3,4),(4,3),(5,4),(4,5),(6,5),(5,6)

Therefore P((X-Y|=1) =10/36

Proceeding similar way  P((X-Y|=2) =8/36; P((X-Y|=3) =6/36; P((X-Y|=4) =4/36, P((X-Y|=5) =2/36

|X-Y|	P(|X-Y|)
0	1/6
1	2/7
2	2/9
3	1/6
4	1/9
5	1/18