### Finite Order Statistic Experiment

#### Description

The experiment consists of selecting \(n\) balls at random (without replacement) from a population of \(m\) balls, numbered from 1 to \(m\). For \(i \in \{1, 2, \ldots, n\}\), the \(i\)th smallest number in the sample, \(X_{(i)}\) (the \(i\)th order statistic), is recorded on each update. For a selected \(k\), the probability density function and moments of \(X_{(k)}\) are shown in the blue in the distribution graph and are recorded in the distribution table. When the simulation runs, the empirical density function and moments of \(X_{(k)}\) are shown in red in the distribution graph and are recorded in the distribution table. The parameters \(m\), \(n\), and \(k\) can be varied with input controls.