Bayesian Statistics: An Introduction, 4th Edition

3.7 The tramcar problem

3.7.1 The discrete uniform distribution

Occasionally, we encounter problems to do with the discrete uniform distribution. We say that x has a discrete uniform distribution on and write

if

One context in which it arises was cited by Jeffreys (1961, Section 4.8). He says,

The following problem was suggested to me several years ago by Professor M. H. A. Newman. A man travelling in a foreign country has to change trains at a junction and goes into the town, of the existence of which he has only just heard. He has no idea of its size. The first thing that he sees is a tramcar numbered 100. What can he infer about the number of tramcars in the town? It may be assumed for the purpose that they are numbered consecutively from 1 upwards.

Clearly, if there are tramcars in the town and you are equally likely to see any one of the tramcars, then the number n of the car you observe has a discrete uniform distribution . Jeffreys suggests that (assuming is not too small) we ...