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Question
The probability distribution of a discrete random variable X is given below:
| X | 2 | 3 | 4 | 5 |
| P(X) | `5/"k"` | `7/"k"` | `9/"k"` | `11/"k"` |
The value of k is ______.
Options
8
16
32
48
Solution
The probability distribution of a discrete random variable X is given below:
| X | 2 | 3 | 4 | 5 |
| P(X) | `5/"k"` | `7/"k"` | `9/"k"` | `11/"k"` |
The value of k is 32.
Explanation:
We know that `sum_("i" = 1)^"n" "P"("X"_"i")` = 1
∴ `5/"k" + 7/"k" + 9/"k" + 11/"k"` = 1
`32/"k"` = 1
⇒ k = 32
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