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Question
A six sided die is marked ‘1’ on one face, ‘3’ on two of its faces, and ‘5’ on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the probability mass function
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Solution
Let X be the random variable denotes the total score in two thrown of a die.
Sample space S
| I\II | 1 | 3 | 3 | 5 | 5 | 5 |
| 1 | 2 | 4 | 4 | 6 | 6 | 6 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 3 | 4 | 6 | 6 | 8 | 8 | 8 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
| 5 | 6 | 8 | 8 | 10 | 10 | 10 |
n(S) = 36
X = {2, 4, 6, 8, 10}
| Values of the random variable | 2 | 4 | 6 | 8 | 10 | Total |
| Number of elements in inverse image | 1 | 4 | 10 | 12 | 9 | 36 |
Probability mass function
| x | 2 | 4 | 6 | 8 | 10 |
| f(x) | `1/36` | `4/36` | `10/36` | `12/36` | `9/36` |
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