The experiment consists of rolling \(n\) dice, each governed by the same probability distribution. The die distribution can be chosen from the selection box; the options are:
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 \(i \in \{1, 2, 3, 4, 5, 6\}\).
right right: face \(i\) has probability \((7 - i) / 21\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).
Random variable \(X_i\) gives the score on die \(i\) and so \(\boldsymbol{X} = \left(X_1, X_2, \ldots, X_n\right)\) is a random sample of size \(n\) from the die distribution. This sequence is recorded in the data table. The number of dice \(n\) can be varied from 1 to 56 with the scrollbar.