# Distribution Function

If X is a discrete random variable whose values are sorted from lowest to highest, the distribution function of the variable X is:

**F(x) = p(X ≤ x) **

The distribution function associates the cumulative probability to each value of the random variable.

The **distribution function** is also commonly referred to as the **cumulative distribution function**.

#### Example

Calculate the probability distribution function for the probable scores that can be obtained by throwing a die.

x | p _{i} |
---|---|

x <1 | 0 |

1≤ x < 2 | |

2≤ x < 3 | |

3≤ x < 4 | |

4≤ x < 5 | |

5≤ x < 6 | |

6≤ x | 1 |