gender dataset could be clusterized using two variables instead of one, but this step involves additional complexity. In the univariate case, we saw that the number of parameters estimated is six: 2 means, 2 standard deviations and 2 proportions.
When we add an additional variable and consider the cross term distinct from zero, we still have to estimate two means, but each of them is formed by two values. Moreover, the covariance matrix is formed by four values; the corresponding variances and the cross term.
How many distinct values should we estimate?