In the nineteenth century, cavalry were still an important part of European military complex. While horses have many wonderful qualities, they can be dangerous beasts, especially if poorly treated. The Prussian army kept track of number of fatalities caused by horse kicks to members of 10 of their cavalry regiments over the 20-year time span. If such fatalities occurred purely by chance, then we would expect number of deaths by horse kick per regiment per year to follow the Poisson distribution. On the other hand, if some regiments throughout some years consisted of particularly bad horsemen, then the events wouldn't be independent; we would thus expect a frequency distribution different from the Poisson distribution. The following shows the data, expressed as the number of fatalities per regiment-year.
Number of deaths (X), Number of regiment-years
0, 109
1, 65
2, 22
3, 3
4, 1
>4, 0
Total: 200
a) Determine the mean number of deaths from horse kicks per regiment-year?
b) Test whether a Poisson distribution fits these data.