1. Correct. The answer is true.
Sample points for the possible sums of the grade points are given in the following table:
Second minerals set |
1, 6 |
2, 6 |
3, 6 |
4, 6 |
5, 6 |
6, 6 |
1, 5 |
2, 5 |
3, 5 |
4, 5 |
5, 5 |
6, 5 |
|
1, 4 |
2, 4 |
3, 4 |
4, 4 |
5,4 |
6, 4 |
|
1, 3 |
2, 3 |
3, 3 |
4, 3 |
5, 3 |
6, 3 |
|
1, 2 |
2, 2 |
3, 2 |
4, 2 |
5, 2 |
6, 2 |
|
1, 1 |
2, 1 |
3, 1 |
4, 1 |
5, 1 |
6, 1 |
|
|
First minerals set |
Then, the random variable X is given by the sum of the coordinates for each point. Thus for (1,3) we have X=4. Using the fact that all 36 sample points are equally probable, so that each sample point has probability of 1/36, we obtain the following table. For example, corresponding X =4 we have three sample points (1,3), (2,2), (3,1), so that the associated probability is 3/36=1/12.
X |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
f(x) |
1/36 |
2/36 |
3/36 |
4/36 |
5/36 |
6/36 |
5/36 |
4/36 |
3/26 |
2/36 |
1/36 |