The experiment consists of selecting \(n\) balls at random from an urn with \(m\) balls, \(r\) of which are red and the other \(m - r\) green. Random variable \(Y\) gives the number of red balls in the sample. Random variable \(U = m Y / n\) is the standard estimate of \(r\) with \(m\) known, and random variable \(V = n r / Y\) is the standard estimate of \(m\) with \(r\) known. The variables \(Y\), \(U\), and \(V\) are recorded in the data table.
Either of two sampling models can be selected with the list box: without replacement and with replacement. In the first case, \(Y\) has the hypergeometric distribution with parameter \(m\), \(n\), and \(r\), and in the second case \(Y\) has the binomial distribution with parameters \(n\) and \(r / m\). The distribution of \(Y\) is described in the distribution graph and table. The parameters \(m\), \(r\), and \(n\) can be varied with the input controls.