#### Description

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 \(i \in \{1, 2, 3, 4, 5, 6\}\).

The following random variables are recorded on each update:

- The sum of the scores \(Y\). This variable illustrates the central limit theorem.
- The average score \(M\). This variable is the sample mean.
- The minimum score \(U\). This variable is the smallest of the order statistics.
- The maximum score \(V\). This variable is the largest of the order statistics.
- The number of aces \(Z\). This variable has a binomial distribution.

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.