In the 19th century, cavalries were still an important part of the European military complex. While horses have many wonderful qualities, they can be dangerous beasts, especially if poorly treated. The Prussian army kept track of the number of fatalities caused by horse kicks to members of 10 of their cavalry regiments over a 20-year time span. If these fatalities occurred independently and with equal probability for each regiment, then the number of deaths by horse kick per regiment per year should follow a Poisson distribution. On the other hand, if some regiments during some years consisted of particularly bad horsemen, then the events would not occur with equal probability, in which case we would expect a frequency distribution different from Poisson distribution. The following table shows the data, expressed as the number of fatalities per regiment-year. Number of deaths (X) Number of regiment-years 0 109 1 65 2 22 3 3 4 1 >4 0 Total 200 What is the mean number of deaths from horse kicks per regiment year? Does Poisson distribution fit these data?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
In the 19th century, cavalries were still an important part of the European military complex. While horses have many wonderful qualities, they can be dangerous beasts, especially if poorly treated. The Prussian army kept track of the number of fatalities caused by horse kicks to members of 10 of their cavalry regiments over a 20-year time span. If these fatalities occurred independently and with equal probability for each regiment, then the number of deaths by horse kick per regiment per year should follow a Poisson distribution. On the other hand, if some regiments during some years consisted of particularly bad horsemen, then the events would not occur with equal probability, in which case we would expect a frequency distribution different from Poisson distribution. The following table shows the data, expressed as the number of fatalities per regiment-year.
|
Number of deaths (X) |
Number of regiment-years |
|
0 |
109 |
|
1 |
65 |
|
2 |
22 |
|
3 |
3 |
|
4 |
1 |
|
>4 |
0 |
|
Total |
200 |
- What is the mean number of deaths from horse kicks per regiment year?
- Does Poisson distribution fit these data?
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
