In the 19th century, cavalries were still an important part of the European military complex. While horses have many wonderful qualities, they can be dangerous beasts, especially if poorly treated. The Prussian army kept track of the number of fatalities caused by horse kicks to members of 10 of their cavalry regiments over a 20-year time span. If these fatalities occurred independently and with equal probability for each regiment, then the number of deaths by horse kick per regiment per year should follow a Poisson distribution. On the other hand, if some regiments during some years consisted of particularly bad horsemen, then the events would not occur with equal probability, in which case we would expect a frequency distribution different from the Poisson distribution. The following table shows the data, expressed as the number of fatalities per regiment-year (Bortkiewicz 1898):

a. What is the mean number of deaths from horse kicks per regiment-year?

b. Test whether a Poisson distribution fits these data.

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Number of deaths (X)(X) 00 11 Number of regiment-years 109109 6565