Note that the random variables Q1, ..., QN in Section 6.3 have a joint multinomial distribution with probabilities 1,42, ..., N. Use properties of the multinomial distribution to show that 4 in (6.13) is an unbiased estimator of t with variance given by v@= (-1) (6.46) Also show that (6.14) is an unbiased estimator of the variance in (6.46). HINT: Use properties of conditional expectation in Appendix A, and write V(t) = V(E[ | Q1QN])+E(V[ | Q1,...,QN]). Consider a without-replacement sample of size 2 from a population of size 4, with joint inclusion probabilities 12 = 34 = 0.31, 13 = : 0.20, 14 = 0.14, 23 = and 24 = 0.01. a Calculate the inclusion probabilities ; for this design. = 0.03, = 2.0, t3 = 1.1, and t4 = 0.5. Find VHT (HT) and SYG (HT) b Suppose t = 2.5, t for each possible sample.