The probability distribution of a discrete random variable shows all of the possible values a discrete random variable can have, along with the corresponding probabilities.￼ You could use a table to organize the information.

In the Discrete Random Variables lesson, you asked 200 people how many vehicles they had. You have come to the following conclusion.

40 people say they don’t own a car, 100 say they have 1 and 60 say they own 2.

You could start with a table that shows the frequency and the relative frequency distribution.

- The relative frequency for owning 0 vehicles is 40/200 = 0.2

- The relative frequency of owning a vehicle is 100/200 = 0.5

- The relative frequency for owning 2 vehicles is 60/200 = 0.3

Number of vehicles owned | Frequency distribution | Relative frequency distribution |

0 | 40 | 0.2 |

1 | 100 | 0.5 |

2 | 60 | 0.3 |

N = 200 | Sum = 1 |

From the table above we can extract the probability distribution. Remember that it lists all possible values for the random variable and their corresponding probabilities.

Number of vehicles owned or x | Probability or P (x) |

0 | 0.2 |

1 | 0.5 |

2 | 0.3 |

= 1 |

## Properties of the probability distribution of a discrete random variable

If you looked closely at the table above, you may have noticed the following 2 characteristics.

- The probability assigned to each value of a discrete random variable is between 0 and 1, inclusive. In other words, 0 P (x) 1

- The sum of the probabilities is equal to 1

**Useful notation**

The meaning of P (x = 1) is the probability that a randomly selected person owns 1 car.

P (x = 1) = 0.5

The meaning of P (x> 0) is the probability that a randomly selected person owns at least 1 car.

P (x> 0) = P (x = 1) + P (x = 2) = 0.5 + 0.3 = 0.8