### Dice Sample Experiment

 Die 1 Die 2 Die 3 Die 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 Die 29 Die 30 Die 31 Die 32 Die 33 Die 34 Die 35 Die 36 Die 37 Die 38 Die 39 Die 40 Die 41 Die 42 Die 43 Die 44 Die 45 Die 46 Die 47 Die 48 Die 49 Die 50 Die 51 Die 52 Die 53 Die 54 Die 55 Die 56

#### Description

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 $$\frac{1}{6}$$.
• 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 $$i \in \{1, 2, 3, 4, 5, 6\}$$.
• right right: face $$i$$ has probability $$\frac{7 - i}{21}$$ for $$i \in \{1, 2, 3, 4, 5, 6\}$$.

Random variable $$X_i$$ gives the score on die $$i$$ and is recorded on each update. These variables form a random sample of size $$n$$ from the die distribution. The number of dice $$n$$ can be varied from 1 to 56 with the scroll bar.