Cauchy Experiment

Distribution graph
Light

Description

A light source is located \( b \) units directly across from position \( a \) on an infinite, straight wall. The random experiment consists of shining the light on the wall at an angle \( \Theta \) with the perpendicular, that is uniformly distributed on the interval \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \). The position \( X = a + b \tan(\Theta) \) of the light beam on the wall has the Cauchy distribution with location parameter \( a \) and scale parameter \( b \). On each run of the experiment, the angle \( \Theta \) and the position \( X \) are recorded in the data table. The probability density function of \( X \) is shown in blue in the distribution graph and is recorded in the distribution table. When the experiment runs, the empirical density function is shown in red in the distribution graph and is recorded in the distribution table. The parameters \( a \) and \( b \) can be varied with the input controls.