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, where \(\Theta\) 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 \( b \). The parameters \( a \) and \( b \) can be varied with the input controls.