Which of the following are True for a random variable?

A. A random variable is a certain quantity, whose value depends on chance.

B. A continuous random variable can assume at most two countable number of values.

C. A discrete random variable can assume at most a countable number of values.

D. A random variable is a function of the sample space.

E. A random variable is an uncertain quantity, whose value depends on chance.

Choose the correct answer:

Correct option is D

· A random variable is a function that assigns numerical values to outcomes of a probability experiment.
· Discrete random variables (C) take countable values (e.g., 0, 1, 2, …).
· Continuous random variables can take infinitely many values over a range (B is incorrect).
· A random variable is a function of the sample space (D), meaning it depends on the probability distribution.
· A random variable is an uncertain quantity (E) as its value depends on chance.