The random variable X has the following probability distribution:
| X | 1 | 2 | 3 | 4 | 5 |
| P(X) | \( \displaystyle\frac{1}{10} \) | \( \displaystyle\frac{1}{10} \) | \( \displaystyle\frac{1}{3} \) | \( k \) | \( \displaystyle\frac{1}{3} \) |
The correct value of \( k \) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{2}{15} \)
The probabilities of a probability distribution add up to 1:
\( \displaystyle \frac{1}{10}+\frac{1}{10}+\frac{1}{3}+k+\frac{1}{3}=1 \)
\( \displaystyle \frac{1}{5}+\frac{2}{3}+k=1 \)
\( \displaystyle \frac{13}{15}+k=1 \)
\( \displaystyle k=\frac{2}{15} \)