5.2-04 – Introductory Statistics – Sheldon M. Ross

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Question:

Suppose a pair of dice is rolled. Let X denote their sum. What are the possible values of X? Assuming that each of the 36 possible outcomes of the experiment is equally likely, what is the probability distribution of X?

Solution:

6
7
8
9
10
11
12
5
6
7
8
9
10
11
4
5
6
7
8
9
10
3
4
5
6
7
8
9
2
3
4
5
6
7
8
1
2
3
4
5
6
7
Dice2
Dice 1
1
2
3
4
5
6

Let X = sum of numbers appearing on the face of a pair of fair dice rolled

Probability distribution of X is as below

X
Frequency
P(X)
2
1
1/36
3
2
2/36
4
3
3/36
5
4
4/36
6
5
5/36
7
6
6/36
8
5
5/36
9
4
4/36
10
3
3/36
11
2
2/36
12
1
1/36
Total
36
1.00


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