AS/A2 Stats 2 Stats 3

S1 Topic 3: Probability
The die and coin experiment
The die coin experiment consists of rolling a die and then tossing a coin the number of times shown on the die. The die score N and the number of heads X are recorded on each update. The density function and moments of X are shown in the blue in the second graph and are recorded in the second table. On each update, the empirical density and moments of X are shown in red in the second graph and are recorded in the second table. The probability of heads p for the coin can be varied with a scroll bar, and any of the following die distributions can be chosen from the list box: 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 = 1, 2, 3, 4, 5, 6. skewed right: face i has probability (7 - i) / 21 for i = 1, 2, 3, 4, 5, 6.

Summary An applet freely available from The Probability/Statistics Object Library