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.