# Random Variable

A random variable is a function that associates a real number to each element of the sample space, **S**.

Capital letters are used X, Y, ... to denote random variables and the lower case letters (x, y, ...) to denote the respective specific values.

### Discrete Random Variable

A **discrete random variable** is one that can only take an **integer value**.

#### Examples

The number of children in a family, the score obtained by throwing a dice.

### Continuous Random Variable

A **continuous random variable** is one that can take **all possible values** within a certain interval.

#### Examples

The height of students in a class, the hours of duration of a battery.

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