Suppose that the population size N is not known, but it is known that n ≤ N. Show that the following procedure will generate a simple random sample of size n. Imagine that the population is arranged in a long list that you can read sequentially.
a. Let the sample initially consist of the the first n elements in the list.
b. For k = 1, 2, . . . , as long as the end of the list has not been encountered:
i. Read the (n + k)-th element in the list.
ii. Place it in the sample with probability n/(n + k) and, if it is placed in the sample, randomly drop one of the exisiting sample members.
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