Consider a probability sample S of n observation units from a population U of N observation units. The weights are wi =1/i, where i is

Consider a probability sample S of n observation units from a population U of N observation units. The weights are wi =1/πi, where πi is the probability that unit I is in the sample. Now let S2 be a subsample of S of size n2, with units selected with probability proportional to wi. Show that S2 is a self-weighting sample from U.