Using maximum likelihood fit a poisson distribution to the...

using maximum likelihood fit a Poisson distribution to the following famous data on the number of deaths from the kick of a horse per army corps per year, for 10 Prussian Army corps for 20 years. The total number of units here, an army corps per year, is n=200. # of deaths from horse kick: 0 1 2 3 4 Observed frequency: 109 65 22 3 1

Deaths from Horse Kicks A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894 . Data for 14 corps were combined for the 20 -year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of deaths per corps-year, find the probability that a randomly selected corps-year has the following numbers of deaths: (a) $0,(\mathbf{b}) 1,(\mathbf{c}) 2$, (d) $3,(\mathrm{e}) 4$. The actual results consisted of these frequencies: 0 deaths (in 144 corps-years); 1 death (in 91 corps-years); 2 deaths (in 32 corps-years); 3 deaths (in 11 corps-years); 4 deaths (in 2 corps-years). Compare the actual results to those expected by using the Poisson probabilities. Does the Poisson distribution serve as a good tool for predicting the actual results?

Discrete Probability Distributions

Poisson Probability Distributions

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