Let be a random sample of five observations from a discrete uniform distribution with pdf . The largest observation is 60 (that is, ).

Then .

Note that L is a monotonically decreasing function of N and so nowhere in the interval is equal to zero. However, note that:

1. L increases as N decreases, and

2. N must be equal to or greater than 60.

Therefore the value of N that maximises L is N = 60 (that is, ).

Note: This estimator is not an unbiased estimator of N.