Description

The coin die experiment consists of first tossing a coin, and then rolling a red die if the coin lands head or a green die if the coin lands tails. Random variable \(X\) gives the coin score (1 for heads and 0 for tails) and random variable \(Y\) gives the die score. The probability distribution that governs the red die and the distribution that governs the green die can be specified with the select boxes; the choices 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 \(i \in \{1, 2, 3, 4, 5, 6\}\).
• skewed right: face \(i\) has probability \((7 - i) / 21\) for \(i \in \{1, 2, 3, 4, 5, 6\}\).

Variables \(X\) and \(Y\) are recorded in the data table, and their distributions are described in the distribution graphs and tables. The probability of heads \(p\) for the coin can be varied with a scrollbar. This app illustrates conditional probability and conditional distributions.