Solution
The German Tank Problem
Show the problem again
An enemy produces tanks with serial numbers 1, 2, ..., N. You capture four tanks with serial numbers 19, 40, 42, and 60. Using the standard minimum-variance unbiased estimator, what is your estimate of N?
Worked solution
The answer is 74. The MVUE for a discrete uniform maximum is N̂ = m + m/k − 1, where m is the sample maximum and k the sample size: intuitively, extend the observed max by the average gap between order statistics. Here m = 60, k = 4: N̂ = 60 + 15 − 1 = 74. Allied statisticians used exactly this in WWII, estimating German tank production far more accurately than intelligence reports.
Source: The German tank problem, from Allied statistical estimation of German production in the Second World War. Statement written for AxiomIQ.