#### Description

This experiment simulates the Cauchy distribution with location parameter \(a\) and scale parameter \(b\) as a random quantile. The graph of the cumulative distribution function \(F\) is shown on the left and the graph of the probability density function \(f\) is shown on the right. On each run, a random number \(U\) (with the standard uniform distribution) is generated and also the random quantile \(X = F^{-1}(U)\). These are shown in the graph on the left and are recorded in the table on the left. As the experiment runs, the empirical density function and empirical moments are illustrated in the graph on the right and recorded in the table on the right. The parameters \(a\) and \(b\) can be varied with the input controls.