In 1898 L. J. Bortkiewicz published a book entitled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution with a mean of 0.63.

Question

(a) What is the probability of more than one death in a corps in a year?

(b) What is the probability of no deaths in a corps over 4 years?

Answer 1

Poisson distribution (m = mean):
P(x) = e^(-m) m^x / x!

Values for (a):
x = 0, 1
m = 0.63

Substitute and calculate for each x. Add those calculations together for a total probability. Then subtract that value from 1. This will give you the probability of more than one death.

For (b):
To determine the number of deaths over 4 years, take (0.63)(4) = 2.52 (this is the mean). Now calculate P(0) using the above formula.

I hope this will help get you started.

Answer 2

0.2845
0.6984