(Requires probability.) Suppose you would like to take an SRS of size n from a list of N units, but do not know the population size N in advance. Consider the following procedure:
a Set S0 = {1, 2, … , n}, so that the initial sample for consideration consists of the first n units on the list.
b For k = 1, 2, …, generate a random number uk between 0 and 1. If uk > n/(n+k), then set Sk equal to Sk−1. If uk ≤ n/(n + k), then select one of the units in Sk−1 at random, and replace it by unit (n + k) to form Sk . Show that SN−n from this procedure is an SRS of size n. Hint: Use induction.
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