Consider a population U of size N. From U, we select a sample, S, of size 71 according to the following sampling design: Unit 1 is included in the sample with certainty (with 1 probability 1). Then, from the N 1 remaining units in the population, we select a sample 8*, of size n 1, according to simple random sampling without replacement. Therefore 5' = {1} U 8". Show that the estimator is unbiased for ty = 2,6,, y,. Hint: Express the sum over S as a sum over U and use the sample selection indicators Z,. Then, you will make use of Proposition 4 with the modied population and sample sizes