Bertrand's Experiment

Bertrand's Floor
Distribution graph

Description

Bertrand's experiment is a random experiment that generates a random chord of a circle. In the simulation, one point of the chord is fixed at \((0, 1)\) and the other random point \((X, Y)\) is recorded on each update in the data table. Also recorded are \(D\), the length of the line segment from the center of the circle to the center of the chord, and \(A\), the angle that this line segment makes with the horizontal. Random variable \(I\) indicates the event that the chord is longer than the length of a side of the inscribed equilateral triangle. 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. One of three models can be selected with the list box: