# The Prussian cavalries (Poisson distribution) In 1898,  the Prussian army wanted to verify if the deaths of soldiers by a horse kick (per year and army unit) is random or not. They model this by random variable that represent the number of death per unit and year. During 20 years, 10 units where observed and 122 deaths occurred. This provided 200 samples of number of years per army unit had 0 death, 1 death, 2 death etc. (see table below in column A) The expectation number of death per year and unit was  𝛌=0.61(=122/200). The column E is the number of deaths per year and army unit according to Poisson distribution i.e., $E=200\times p$ for $\lambda=0.61$. The column A is the actual number of army units samples with K=0,..,6 deaths. ![[Pasted image 20240628111001.png|281]] As can seen, A and E are similar and so it is reasonable to assume they occurred in random and there is no much one can do the reduce them. ## Created 2025-02-28 15:55