The experiment consists of rolling \(n\) dice, each governed by the same probability distribution. You can choose among the following special distributions:

fair: each face has probability \(\frac{1}{6}\).

1-6 flat: faces 1 and 6 have probability \(\frac{1}{4}\) each; faces 2, 3, 4, and 5 have probability \(\frac{1}{8}\) each.

2-5 flat: faces 2 and 5 have probability \(\frac{1}{4}\) each; faces 1, 3, 4, and 6 have probability \(\frac{1}{8}\) each.

3-4 flat: faces 3 and 4 have probability \(\frac{1}{4}\) each; faces 1, 2, 5, and 6 have probability \(\frac{1}{8}\) each.

skewed left: face \(i\) has probability \(\frac{i}{21}\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).

skewed left: face \(i\) has probability \(\frac{7 - i}{21}\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).

Any one of these variables can be selected with a list box. The probability density function 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 function 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.