Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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