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Question
Solve the following problem :
The probability distribution of a discrete r.v. X is as follows.
| X | 1 | 2 | 3 | 4 | 5 | 6 |
| (X = x) | k | 2k | 3k | 4k | 5k | 6k |
Determine the value of k.
Solution
Since P(X) is the probability distribution of X,
\[\sum\limits_{x =1}^{6}\text{P}(X = x) = 1\]
∴ k + 2k + 3k + 4k + 5k + 6k = 1
∴ 21k = 1
∴ k = `(1)/(21)`.
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