## Distributions With Two Random Variables

For distributions with two random variables, we examine the probabilities regarding possible values of respective variables. As an example, two discrete random variables X and Y representing the top and bottom numbers of a fair die when tossed, may be addressed as follows:

Y = 1 | Y = 2 | Y = 3 | Y = 4 | Y = 5 | Y = 6 | |

X = 1 | 0 | 0 | 0 | 0 | 0 | 1/6 |

X = 2 | 0 | 0 | 0 | 0 | 1/6 | 0 |

X = 3 | 0 | 0 | 0 | 1/6 | 0 | 0 |

X = 4 | 0 | 0 | 1/6 | 0 | 0 | 0 |

X = 5 | 0 | 1/6 | 0 | 0 | 0 | 0 |

X = 6 | 1/6 | 0 | 0 | 0 | 0 | 0 |

The above table of probabilities was based upon the facts the die being tossed is fair and sum of top and bottom numbers of a die always equal seven.

Similar to distributions with single random variables, probability density functions and cumulative distribution functions are applicable distributions with two random variables. In addition, the two random variables may be either discrete or continuous.

Related Topics:

- Joint Probability Density Function
- Joint Cumulative Distribution Function
- Marginal Density Function