The probability distribution of a random variable X is given below
| X | 0 | 1 | 2 | 3 |
| P(X = x) | k | \(\displaystyle\frac{k}{2}\) | \(\displaystyle\frac{k}{4}\) | \(\displaystyle\frac{k}{8}\) |
Then \(P(X \le 2)\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\frac{14}{15}\)
The probabilities add up to 1:
\( \displaystyle k + \frac{k}{2} + \frac{k}{4} + \frac{k}{8} = 1 \)
\( \displaystyle \frac{15k}{8} = 1 \)
\( \displaystyle k = \frac{8}{15} \)
The only value above 2 is X = 3, so by the complement:
\( \displaystyle P(X \le 2) = 1 - P(X = 3) = 1 - \frac{k}{8} \)
\( \displaystyle = 1 - \frac{1}{15} = \frac{14}{15} \)