I have been looking through the German Tank Problem recently, There are many videos and references regarding this problem but what got me thinking is that I know that at first, the Maximum Likelihood Estimator is equal to the maximum of the sample.
I also understand that this comes from a Uniform Discrete Distribution without replacement. I have been trying to find resources to help me with finding the Expectation and the Variance of the estimator X(m) where X(m) is the maximum of the sample.
I have been looking up order statistics regarding the discrete uniform distribution without replacement but couldn't find anything related. Would really appreciate some guidance or links that I can look up on the Expectation and the Variance of this estimator.