Which is the most suitable definition for random variable among the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → It is a function defined from the sample space of a random experiment to the set of real numbers.
A random variable is a real-valued function whose domain is the sample space of a random experiment: it assigns a real number to each outcome. For example, in tossing two coins, X = number of heads assigns 0, 1 or 2 to each outcome.
Why the other options are incorrect
Option (1) It is a relation between the events of a sample space and the numbers in [0,1]. — Incorrect. Assigning numbers in [0, 1] to events describes probability, not a random variable, whose values can be any real numbers.
Option (3) It is a table containing probability values — Incorrect. Such a table is the probability distribution of a random variable, not the random variable itself.
Option (4) It is a function from the set of natural numbers to the numbers in [0,1] — Incorrect. The domain of a random variable is the sample space, not the natural numbers, and its values are not limited to [0, 1].
NCERT (2026-27 edition):
Bayes' Theorem
