2.12. To estimate the average income per household (_vy,/N) for a population of N = 200 households, a listing of the 600 persons that belong to the 200 house- holds was used as follows. An SIR sample of size m = 10 persons was drawn. The households of the selected persons were identified, and information on average household income, yx/xx, was collected, where y, is the total household income in dollars, and x, is the number of persons in the household. The results are as follows: Draw Average household income (yx,/Xx,) 7,000 8,000 6,000 5,000 9,000 4,000 7,000 8,000 4,000 2,000 Compute an estimate of the average income per household based on the pwr estimator as well as the corresponding cue. 213 Show that the second-order inclusion probabilities for gener with-replacement