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Question
The expected value of the sum of two numbers obtained when two fair dice are rolled is ______.
Options
5
6
7
8
Solution
The expected value of the sum of two numbers obtained when two fair dice are rolled is 7.
Explanation:
The sample space of the experiment consists of 36 elementary events in the form of ordered pairs (xi, yi), where xi = 1, 2, 3, 4, 5, 6 and yi = 1, 2, 3, 4, 5, 6.
The random variable X, i.e., the sum of the numbers on the two dice takes the values 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12.
| X = xi | P(xi) | xiP(xi) |
| 2 | `(1)/(36)` | `(2)/(36)` |
| 3 | `(2)/(36)` | `(6)/(36)` |
| 4 | `(3)/(36)` | `(12)/(36)` |
| 5 | `(4)/(36)` | `(20)/(36)` |
| 6 | `(5)/(36)` | `(30)/(36)` |
| 7 | `(6)/(36)` | `(42)/(36)` |
| 8 | `(5)/(36)` | `(40)/(36)` |
| 9 | `(4)/(36)` | `(36)/(36)` |
| 10 | `(3)/(36)` | `(30)/(36)` |
| 11 | `(2)/(36)` | `(22)/(36)` |
| 12 | `(1)/(36)` | `(12)/(36)` |
| E(X) = \[\sum\limits_{i=1}^{n} x_i\text{P}(x_i)\] = `(252)/(36)` = 7 |
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