Suppose that x x1 xn is a simple random sample without

Question

Suppose that X = (X₁, ..., X_n) is a simple random sample (without replacement) from a finite population P = {y₁, ..., y_N} with univariate y_i.

(a) Show that a necessary condition for h(θ) to be estimable is that h is symmetric in its N arguments.

(b) Find the UMVUE of Y_m, where m is a fixed positive integer < n="" and="" y="" is="" the="" population="" total.="">

(c) Find the UMVUE of P(X_i ≤ X_j), i ≠ j.

(d) Find the UMVUE of Cov(X_i, X_j), i ≠ j.