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 \(i \in \{1, 2, 3, 4, 5, 6\}\).