# Math Help - German Tank Problem

1. ## German Tank Problem

Hi, I was reading the article on Wikipedia regarding the German Tank Problem.

German tank problem - Wikipedia, the free encyclopedia

Under the section of "Frequentist analysis", sub-section "Derivation", it states that the probability that the sample maximum equals m is:

$P(M=m | N=n,K=k) = \frac { \binom {m-1}{k-1}}{ \binom {n}{k}}$

where m is the sample maximum, n is the size of the population, k is number of observed samples.

I just don't quite understand how this formula comes to being...

Thanks~!!!

2. ## Re: German Tank Problem

You might want to look at the definition of estimators for estimating the parameter of a discrete uniform distribution:

https://en.wikipedia.org/wiki/Maximu...m_distribution

In terms of the distribution of the maximum, you should look at the order statistics:

Order statistic - Wikipedia, the free encyclopedia