In 1898, Ladislaus Bortkiewicz, a Polish statistician, studied the distribution
ID: 3221510 • Letter: I
Question
In 1898, Ladislaus Bortkiewicz, a Polish statistician, studied the distribution of solider deaths
by horse kicks in the Prussian calvary. He found that the average number of deaths per corps-
year was 0.61 (122 deaths in 200 corps-years). Let X be the number of deaths by horse kick
per year.
(a) Describe the distribution of X. Then nd the mean and variance of X.
(b) What is the probability of 3 deaths by horse kick in a year?
(c) What is the probability of at least 1 death by horse kick in a year (Hint: Find the
complement)?
Explanation / Answer
Solution:-
(a) The distribution of X is poisons distribution. Then mean and variance of X is 0.61 and 0.61.
This is poisons distribution.
Mean of the poisons distribution is
= 0.61
2 = 0.61
(b) The probability of 3 deaths by horse kick in a year is 0.021.
P(x; ) = (e-) (x) / x!
P(x = 3) = 0.021
(c) The probability of at least 1 death by horse kick in a year is 0.4567.
P(x; ) = (e-) (x) / x!
P(x > 1) = 0.4567