Is Poisson Distribution Relevant for Analyzing 19th Century Cavalry Deaths?

[OguzhanCatal]

Doing Physics at University and I have never done poisson distributions.
How the hell do I do it?
The question is...
Show that the data on the number of cavalry deaths in the Prussian Army in the 19th Century are consistent with the poisson probability distribution. The date were accumulated from reports received from 10 separate cavalry corps, yearly, over a 20 year period.
There were: 109 Reports of ZERO deaths, 65 reports of 1 death, 22 reports of 2 deaths, 3 reports of 3 deaths and 1 report of 4 deaths.

Where do I begin? Does it involve drawing a graph?!

 

[Nate810]

Yes, it does involve drawing a graph. To begin, you need to calculate the expected mean value of the data. This can be done by multiplying the total number of cavalry deaths by the probability of each outcome. For example, 109 x 0% (probability of zero deaths) = 0. Then add up all the expected values to get the mean. Once you have the mean, you can plot the poisson distribution for the given mean on a graph using a graphing calculator or an online graphing tool. The graph should show the probability of each outcome (e.g. 0, 1, 2, 3, 4 deaths) on the y-axis and the number of reports on the x-axis. If the data points match up to the poisson distribution, then it is consistent with the distribution.

 

[ogb p]

First of all, don't panic! Poisson distribution may seem intimidating at first, but with some guidance, it can be easily understood and applied.

To begin, let's first understand what a Poisson distribution is. It is a probability distribution that is used to model the number of events that occur in a given time or space interval. It is often used in situations where the events occur independently and at a constant rate.

Now, let's look at the given data. We have a total of 200 reports (10 corps x 20 years) and the number of cavalry deaths in each report. The data is already sorted in ascending order, which is helpful for our analysis.

To show that the data is consistent with the Poisson distribution, we need to calculate the expected number of events (cavalry deaths) for each given number of reports (i.e. 0, 1, 2, 3, 4). This can be done using the Poisson probability formula:

P(x) = (e^-λ * λ^x) / x!

Where:
- P(x) is the probability of x events occurring
- e is the base of natural logarithm (approximately equal to 2.718)
- λ is the average number of events in a given time or space interval
- x is the number of events we are interested in

In this case, we can estimate λ by dividing the total number of cavalry deaths (93) by the total number of reports (200). This gives us an average of 0.465 cavalry deaths per report.

Now, we can plug in the values of λ and x into the formula for each given number of reports and calculate the expected number of events. For example, for 109 reports of zero deaths, the expected number would be:

P(0) = (e^-0.465 * 0.465^0) / 0! = 0.628

Similarly, we can calculate the expected number for 65 reports of 1 death, 22 reports of 2 deaths, 3 reports of 3 deaths, and 1 report of 4 deaths.

Once we have calculated the expected numbers, we can compare them with the actual numbers given in the data. If they are close, then it is an indication that the data is consistent with the Poisson distribution.

To visually represent this, you can plot a bar graph with the expected numbers on the y-axis and