| x↓y→ |
1 |
2 |
TOTAL |
| 1 |
2/21 |
1/7 |
5/21 |
| 2 |
1/7 |
4/21 |
1/3 |
| 3 |
4/21 |
5/21 |
3/7 |
| TOTAL |
3/7 |
4/7 |
1 |
Table shows all possibilities and validates P(x,y)=(x+y)/21 because ∑P(x,y)=1 for X∈{1,2,3} and Y∈{1,2}.
When X=1, we can find E[Y]=1(2/21)+2(1/7)=2/21+2/7=8/21.
E[Y²]=1(2/21)+4(1/7)=2/21+4/7=14/21=2/3.
VAR=2/3-(8/21)²=230/441.