The probability distribution of a random variable x is given below.
| x | 0 | 1 | 2 | 3 |
| P(x) | k/3 | k/2 | k/4 | k/7 |
Then the value of k is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{84}{103}\)
In a probability distribution the probabilities add up to 1:
\( \displaystyle \frac{k}{3} + \frac{k}{2} + \frac{k}{4} + \frac{k}{7} = 1 \)
With the LCM 84:
\( \displaystyle \frac{28k + 42k + 21k + 12k}{84} = 1 \)
\( \displaystyle \frac{103k}{84} = 1 \)
\( \displaystyle k = \frac{84}{103} \)