The experiment is to draw a random sample of size \(n\) with replacement from a population of size \(m\). In the app, the population consists of \(m\) balls numbered from 1 to \(m\). The random variables of interest are \(V\), the number of distinct values in the sample, and \(I\), the indicator variable that indicates at least one duplication in the sample (the birthday event). These variables are recorded in the data table and their distributions described in the distribution graphs and tables. The parameters \(m\) and \(n\) can be varied with scrollbars.