Buffon's Coin Experiment

Buffon's Floor
Scatter plot
Cross distribution graph

Description

Buffon's coin experiment is a random experiment in which a coin is tossed on a floor with square tiles. The experiment is shown graphically in the picture box. Random variables \(X\) and \(Y\) are the coordinates of the center of the coin relative to the center of the square. These variables are recorded on each update in the data table, and the corresponding point is shown graphically as a red dot in the scatterplot. Random variable \(I\) indicates the event that the coin crosses a crack, and is recorded on each update in the data table. The probability density function of \(I\) is shown in blue in the distribution graph, and is recorded in the distribution table. On each update, the empirical density function of \(I\) is shown in red in the distribution graph, and is recorded in the distribution table. The parameter of the process is the radius \(r\) of the coin, which can be varied with the scroll bar.