# What is a random variable? What is an example of a discrete random variable and a continuous random variable?

##### 1 Answer

Random Variable is a real valued function on the sample space, taking values on the real line (-∞,∞)

#### Explanation:

A **random variable** is a real number associated with the outcomes of a random experiment. eg. if a die is rolled and X denotes the number obtained on the die, then X is a random variable which can result in any of the following values 1,2,3,4,5 or 6, each with equal probability.

**Discrete Random Variable:** A random variable that assumes only a finite or countable number of possible values.

*E.g. Marks obtained by a student in a test from 100 (the possibile marks would be from 0 to 100 and thus is countable)
It has a countable number of possible values.*

**Continuous Random Variable:** A random variable that can assume an infinite and uncountable set of values.

*E.g. Height of students in a class, Time it takes to travel from one point to another*

It can take all values in a given interval of numbers.

Here we usually mean any value within a particular interval and not at a point.

Discrete Random Variables represent counted data and Continuous Random Variables represent measured data.