數學題,,,

The possible outcomes of throwing two dice are
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Since we roll a pair of balanced dice, the possible values of X and Y are 0,1,2 respectively
For X=0, Y=0 suitable outcomes are
(2,2) (2,3) (3,2) (3,3)
For X=0, Y=1 suitable outcomes are
(2,4) (2,5) (2,6) (3,4) (3,5) (3,6) (4,2) (4,3) (5,2) (5,3) (6,2) (6,3)
For X=0, Y=2 suitable outcomes are
(4,4) (4,5) (4,6) (5,4) (5,5) (5,6) (6,4) (6,5) (6,6)
For X=1, Y=0 suitable outcomes are
(1,2) (1,3) (2,1) (3,1)
For X=1, Y=1 suitable outcomes are
(1,4) (1,5) (1,6) (4,1) (5,1) (6,1)
For X=1, Y=2 suitable outcome is 0
For X=2, Y=0 suitable outcome is
(1,1)
For X=2, Y=1 suitable outcome is
For X=2, Y=2 suitable outcome is 0
The joint probability distribution table of X and Y is






X/Y
0
1
2

0
4/36
12/36
9/36

1
4/36
6/36
0

2
1/36
0
0