There are 11064 Cars in Luxembourg

I was in Luxembourg recently and saw 4 cars when I was there. Their registration plates were 1396, 1871, 2383 and 8852

This made me wonder if I could estimate the total number of cars in Luxembourg. 

This is the German Tank problem where the British in WW2 found some serial numbers on German tanks in north Africa and wanted to use those to guess how many tanks had been produced. If you are sure the serial number on tanks goes up by one each time and they started with number 1. Then if you have seen the highest number 100 in looking at 3 tanks of after looking at 50 you can have a better estimate to the highest number of tank made.  Also if you see a tank with number 1000 you know at least 1000 have been made. 

A formula to estimate the total number based on seeing k serial (registration) numbers where m is the highest number seen is the MVUE (Minimum Variance Unbiased Estimator) N ≈ m + (m/k − 1)

Which gives an estimate of 11064 total cars in Luxembourg.