The experiment consists of rolling n dice, each governed by the same probability distribution. Any of the following die distributions can be chosen from the list box:

* fair: each face has probability 1/6

* 1-6 flat: faces 1 and 6 have probability 1/4 each; faces 2, 3, 4, and 5 have probability 1/8 each.

* 2-5 flat: faces 2 and 5 have probability 1/4 each; faces 1, 3, 4, and 6 have probability 1/8 each.

* 3-4 flat: faces 3 and 4 have probability 1/4 each; faces 1, 2, 5, and 6 have probability 1/8 each.

* skewed left: face i has probability i / 21 for i = 1, 2, 3, 4, 5, 6.

* skewed right: face i has probability (7 - i) / 21 for i = 1, 2, 3, 4, 5, 6.

The following random variables are recorded on each update:

* The sum of the scores Y.

* The average score M.

* The minimum score U.

* The maximum score V.

* The number of aces (1's) Z.

Any one of these variables can be selected with a list box. The density and moments of the selected variable are shown in blue in the distribution graph and are recorded in the distribution table. When the simulation runs, the empirical density and moments are shown in red in the distribution graph and are recorded in the distribution table. The parameter n can be varied with a scroll bar.

* fair: each face has probability 1/6

* 1-6 flat: faces 1 and 6 have probability 1/4 each; faces 2, 3, 4, and 5 have probability 1/8 each.

* 2-5 flat: faces 2 and 5 have probability 1/4 each; faces 1, 3, 4, and 6 have probability 1/8 each.

* 3-4 flat: faces 3 and 4 have probability 1/4 each; faces 1, 2, 5, and 6 have probability 1/8 each.

* skewed left: face i has probability i / 21 for i = 1, 2, 3, 4, 5, 6.

* skewed right: face i has probability (7 - i) / 21 for i = 1, 2, 3, 4, 5, 6.

The following random variables are recorded on each update:

* The sum of the scores Y.

* The average score M.

* The minimum score U.

* The maximum score V.

* The number of aces (1's) Z.

Any one of these variables can be selected with a list box. The density and moments of the selected variable are shown in blue in the distribution graph and are recorded in the distribution table. When the simulation runs, the empirical density and moments are shown in red in the distribution graph and are recorded in the distribution table. The parameter n can be varied with a scroll bar.

## Summary/Background

In the case where the faces of all dice have equal probability of coming up, the distribution is a uniform one.

## Software/Applets used on this page

## Glossary

### density

the ratio of the mass of an object to its volume

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### parameter

a) a constant or variable term in a function that determines the specific form of the function but not its general nature, as a in f(x) = ax, where a determines only the slope of the line described by f(x).

b) one of the independent variables in a set of parametric equations.

b) one of the independent variables in a set of parametric equations.

### variable

A value which is unknown and free to vary, often denoted by x or y.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S2 | Discrete Random Variables | Uniform Distribution | - |

AQA A2 Further Maths 2017 | Statistics | Continuous Random Variables | The Uniform Distribution | - |

AQA AS/A2 Further Maths 2017 | Statistics | Continuous Random Variables | The Uniform Distribution | - |

CCEA A-Level (NI) | S1 | Discrete Random Variables | Uniform Distribution | - |

CIE A-Level (UK) | S1 | Discrete Random Variables | Uniform Distribution | - |

Edexcel A-Level (UK - Pre-2017) | S1 | Discrete Random Variables | Uniform Distribution | - |

Edexcel AS Further Maths 2017 | Further Statistics 2 | Continuous Distributions | The Uniform Distribution | - |

Edexcel AS/A2 Further Maths 2017 | Further Statistics 2 | Continuous Distributions | The Uniform Distribution | - |

I.B. Higher Level | 7 | Discrete Random Variables | Uniform Distribution | - |

I.B. Standard Level | 5 | Discrete Random Variables | Uniform Distribution | - |

Methods (UK) | M14 | Discrete Random Variables | Uniform Distribution | - |

OCR A-Level (UK - Pre-2017) | S1 | Discrete Random Variables | Uniform Distribution | - |

OCR A2 Further Maths 2017 | Statistics | Continuous Random Variables | The Uniform Distribution | - |

OCR MEI A2 Further Maths 2017 | Statistics B | Continuous Random Variables | The Uniform Distribution | - |

OCR-MEI A-Level (UK - Pre-2017) | S1 | Discrete Random Variables | Uniform Distribution | - |

Scottish (Highers + Advanced) | HS | Discrete Random Variables | Uniform Distribution | - |

Scottish Highers | S | Discrete Random Variables | Uniform Distribution | - |

Universal (all site questions) | D | Discrete Random Variables | Uniform Distribution | - |

WJEC A-Level (Wales) | S1 | Discrete Random Variables | Uniform Distribution | - |