The advice sometimes given for the validity of the \(\chi^{2}\) approximation to the null distribution of Pearson's statistic is that the minimum expected value should exceed a suitable threshold, usually in the range 3-5. However, the mean count for the birth-death table is 2.42 , so the expected count in every cell falls below the threshold. Compute the null distribution of Pearson's statistic by hypergeometric simulation. Plot the density histogram of simulated values, and superimpose on it the \(\chi_{121}^{2}\) density function. (This is intended as a computational exercise only. It is not a suggestion for data analysis aimed to address the question posed by Phillips and Feldman.)