Stop: 10 Stop: 100 Stop: 1000 Stop: 10000 Stop: never Show Distribution

Fair 1-6 flat 2-5 flat 3-4 flat skewed left skewed right Y: sum of scores M: average score U: minimum score V: maximum score Z: number of aces

Die 1 Die 2 Die 3 Di3 4 Die 5 Die 6 Die 7 Die 8 Die 9 Die 10 Die 11 Die 12 Die 13 Die 14 Die 15 Die 16 Die 17 Die 18 Die 19 Die 20 Die 21 Die 22 Die 23 Die 24 Die 25 Die 26 Die 27 Die 28	Distribution graph

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.