The Dice Experiment

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.