# Suppose you would like to take an SRS of size n from a list of N units, but do not

## Question:

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 S_{0} = {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 u_{k} >n / (n+k), then set Sk equal to S_{k−1}. If u_{k} ≤ 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 S_{N−n} from this procedure is an SRS of size n. Hint: Use induction.

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