Consider a population U of size N. From U, we select a sample._ .3, of size :11 acoording to a sampling design with rst-order inclusion probabilities n,- and secondorder iuthsiou probabilities 1r,- -_. t' a 3'. For which nite population parameter is the following estimator unbiased? Simplify your answer and you will obtain a familiar parameter. Hint: Express all the sums over S as sums over U and use the sample selection indicators 31-. Then. you will make use of Proposition 2 in the course notes. Proposition 2. The sample selection indicators Z, satisfy the following properties: () E(Z) = 1; () V(Z) = m(1-a); (mii) E(Z,Z,) = ny fori # j: (iv) Coo(Z,, Z,) = my - min, fori # j