Which of the following can be the probability distribution of a random variable ?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) →
| X | 0 | 1 | 2 |
| P(X) | 0.4 | 0.2 | 0.4 |
A table is a probability distribution only if
every probability is between 0 and 1, and
the probabilities add up to 1.
For Option (4):
\(0.4 + 0.2 + 0.4 = 1\)
and every value lies between 0 and 1, so it is a probability distribution.
Why the other options are incorrect
Option (1) P(X) = −0.5, 0.5, 0.1 for X = 1, 2, 3 — Incorrect. A probability cannot be negative (−0.5).
Option (2) P(X) = 0.1, 0.4, 0.05, −0.2, 0.2 for X = 1, 2, 3, 4, 5 — Incorrect. A probability cannot be negative (−0.2).
Option (3) P(X) = 0.2, 0.3, 0.2, 0.2 for X = 1, 2, 3, 5 — Incorrect. The probabilities add up to 0.9, not 1.