A random variable X has the following probability distribution
| X | 0 | 1 | 2 | 3 | 4 | 5 |
| P(X) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Then \(P (X \lt 3)\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.4
The probabilities add up to 1:
\(0.1 + k + 0.2 + 2k + 0.3 + k = 1\)
\(0.6 + 4k = 1,\quad k = 0.1\)
X < 3 means X = 0, 1 or 2:
\(P(X \lt 3) = 0.1 + k + 0.2\)
\(= 0.1 + 0.1 + 0.2 = 0.4\)