If two dice are tossed the possible outcomes are 1,2,3,4,5,6 on
each die. To obtain sum and product.
| Dice 1 |
Dice 2 |
X (sum ) |
Y (product) |
| 1 |
1 |
2 |
1 |
| 1 |
2 |
3 |
2 |
| 1 |
3 |
4 |
3 |
| 1 |
4 |
5 |
4 |
| 1 |
5 |
6 |
5 |
| 1 |
6 |
7 |
6 |
| 2 |
1 |
3 |
2 |
| 2 |
2 |
4 |
4 |
| 2 |
3 |
5 |
6 |
| 2 |
4 |
6 |
8 |
| 2 |
5 |
7 |
10 |
| 2 |
6 |
8 |
12 |
| 3 |
1 |
4 |
3 |
| 3 |
2 |
5 |
6 |
| 3 |
3 |
6 |
9 |
| 3 |
4 |
7 |
12 |
| 3 |
5 |
8 |
15 |
| 3 |
6 |
9 |
18 |
| 4 |
1 |
5 |
4 |
| 4 |
2 |
6 |
8 |
| 4 |
3 |
7 |
12 |
| 4 |
4 |
8 |
16 |
| 4 |
5 |
9 |
20 |
| 4 |
6 |
10 |
24 |
| 5 |
1 |
6 |
5 |
| 5 |
2 |
7 |
10 |
| 5 |
3 |
8 |
15 |
| 5 |
4 |
9 |
20 |
| 5 |
5 |
10 |
25 |
| 5 |
6 |
11 |
30 |
| 6 |
1 |
7 |
6 |
| 6 |
2 |
8 |
12 |
| 6 |
3 |
9 |
18 |
| 6 |
4 |
10 |
24 |
| 6 |
5 |
11 |
30 |
| 6 |
6 |
12 |
36 |
table for X
| X value (x) |
Frequency (f) |
x*f |
| 2 |
1 |
2 |
| 3 |
2 |
6 |
| 4 |
3 |
12 |
| 5 |
4 |
20 |
| 6 |
5 |
30 |
| 7 |
6 |
42 |
| 8 |
5 |
40 |
| 9 |
4 |
36 |
| 10 |
3 |
30 |
| 11 |
2 |
22 |
| 12 |
1 |
12 |
| Total |
36 |
252 |
E(x) = sum(f*x)/sum(f) = 252/36 = 7
table for Y
| Y value (y) |
Frequency (f) |
f*y |
| 1 |
1 |
1 |
| 2 |
2 |
4 |
| 3 |
2 |
6 |
| 4 |
3 |
12 |
| 5 |
2 |
10 |
| 6 |
4 |
24 |
| 8 |
2 |
16 |
| 9 |
1 |
9 |
| 10 |
2 |
20 |
| 12 |
4 |
48 |
| 15 |
2 |
30 |
| 16 |
1 |
16 |
| 18 |
2 |
36 |
| 20 |
2 |
40 |
| 24 |
2 |
48 |
| 25 |
1 |
25 |
| 30 |
2 |
60 |
| 36 |
1 |
36 |
| Total |
36 |
441 |
E(y) = sum(f*y)/sum(f) = 441/36 = 12.25
E(X+ 3Y) = E(X) + 3*E(Y) = 7 + 12.25*3 = 7 + 36.75 =
43.75
