The Die Coin Experiment

]> The Die Coin Experiment

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. You can specify the die distribution by clicking on the die probability button; this button bring up the die probability dialog box. You can define your own distribution by typing probabilities into the text fields of the dialog box (but be sure to press enter after typing each probability). Alternately, you can click on one of the buttons in the dialog box to specify one of the following special distributions:

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 $1 8$ .
2-5 flat: faces 2 and 5 have probability $1 4$ ; 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 $i 123456$ .
skewed left: face $i$ has probability $7 i 21$ for $i 123456$ .

This experiment illustrates conditional probability and conditional distributions.