### Random Variable Definition

If S is the sample space of a random experiment and to each s_{i} belongs to S there corresponds unique real number X(s_{i}), then the real valued function s thus defined is called a random variable defined on S.

### Values of a Random Variable

Suppose R is range of a random variable X and R = {x_{1}, x_{2},…..,x_{n}}then (x_{1}, x_{2},…..,x_{n}) are called values of the random variable X.

### Frequency of a Random Variable

Suppose X is a random variable defined on a sample space S. If x_{1}, x_{2},…..,x_{n} are values of S and if f_{i} simple events are corresponding to the same value X_{i} of X for i=1 to n, then f_{1}, f_{2},……,f_{n} are called frequencies of x_{1}, x_{2},…..,x_{n} respectively.

#### Note :-

S is a sample space of a random experiment. N is the number of simple events on S. x_{1}, x_{2},…..,x_{n} are values of X and f_{1}, f_{2},……,f_{n} are corresponding frequencies then