### 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:

• the distance $$D$$ is uniformly distributed
• the angle $$A$$ is uniformly distributed
• the coordinate $$X$$ is uniformly distributed