### Die-Coin Experiment

Die Coin 1 Coin 2 Coin 3 Coin 4 Coin 5 Coin 6
Distribution graph

#### Description

The die coin experiment consists of rolling a die and then tossing a coin the number of times shown on the die. Random variable $$N$$ gives the die score and random variable $$Y$$ gives the number of heads; these are recorded on each update in the data table. The probability density function and moments of $$Y$$ are shown in the blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density function and moments of $$Y$$ are shown in red in the distribution graph and are recorded in the distribution table.

The probability of heads $$p$$ for the coin can be varied with a scroll bar. The die distribution can be chosen with the selection control. The following choices are available:

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

This experiment illustrates conditional probability and conditional distributions.