A random variable X has the following probability distribution :
| x | 1 | 2 | 3 | 4 | 5 |
| P(X = x) | K | K | 3K | \(2K^2\) | \(4K^2\) |
Based on the above information, the value of ‘K’ is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{1}{6}\)
The probabilities add up to 1:
\(K + K + 3K + 2K^2 + 4K^2 = 1\)
\(6K^2 + 5K - 1 = 0\)
\((6K - 1)(K + 1) = 0\)
\( \displaystyle K = \frac{1}{6} \text{ or } K = -1 \)
A probability cannot be negative, so K = −1 is rejected and \(K = \frac{1}{6}\).