aez-notes

(a) A railroad numbers its locomotives in order, \(1,2,\dots,N\). One day you see a locomotive and its number is 60. Guess how many locomotives the company has. (b) You have looked at \(5\) locomotives and the largest number observed is 60. Again guess how many locomotives the company has.

The maximum likelihood estimate is \(60\) in both cases, for this problem you would probably want to use a Bayesian approach.