Agresti, problem 1.10. Calculate both likelihood ratio and Pearson chi-square test statistics and the corresponding P-values. For the former, use 0 log(0) = 0, which makes sense because x log(x) ? 0 as x ? 0. Should we expect good asymptotic approximation here?

1.10 Table 1.3 contains Ladislaus von Bortkiewicz's data on deaths of soldiers in the Prussian army from kicks by army mules (Fisher 1934, Quine and Seneta 1987). The data refer to 10 army corps, each observed for 20 years. In 109 corps-years of exposure, there were no deaths, in 65 corps-years there was one death, and so on. Estimate the mean and test whether probabilities of occurrences in these five categories follow a Poisson distribution (truncated for 4 and above).Table 1.3 Data on Deaths by Mule Kicks, for Exercise 1.10 Number of Deaths Number of Corps-Years 0 109 l 65 2 22 3 3 4 1 25 0