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

The random variables of interest are:

• 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.

These are recorded in the data table, and the distribution of the selected variable is described in the distribution graph and table. The parameter \(n\) can be varied with a scrollbar.