# Random Variable

The outcomes of an experiment are represented by a random variable if these outcomes are numerical or if real numbers can be assigned to them.

For example, in a die rolling experiment, the corresponding random variable is represented by the set of outcomes {1, 2, 3, 4, 5, 6}; while in the coin tossing experiment the outcomes head (H) or tail (T) can be represented as a random variable by assuming 0 to T and 1 to H.

**A random variable is a real valued function that maps the sample space into the real line.**

If S is a sample space with a probability measure and X is a real valued function defined over the elements of S, then X is called a random variable. A random variable is also called a chance variable or a stochastic variable.

### Types of Random Variables

- Discrete Random variable
- Continuous Random variable

**Discrete Random Variable**

If a random variable takes only a finite or a countable number of values, it is called a discrete random variable.

**Continuous Random Variable**

Random Variable Xis said to be continuous if it can take all possible values between certain given limits.