The probability distribution of a random variable X is given by
|
X |
0 |
1 |
2 |
|
P(X) |
k |
2k |
3k |
If $k > 0$, then $P(0 < X ≤ 2)$ is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{5}{6}$
Given the probability distribution:
X: 0 1 2
P(X): k 2k 3k
The total probability must be 1:
$k + 2k + 3k = 6k = 1 \Rightarrow k = \frac{1}{6}$
Now, compute $P(0 < X \leq 2) = P(1) + P(2)$
$= 2k + 3k = 5k = 5 \cdot \frac{1}{6} = \frac{5}{6}$