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 0 03, and 24 0 01 a Calculate the inclusion probabilities i for this design b Suppose t1 2 5, t2 2 0, t3 1 1, and t4 0 5 Find HT (tHT) and SYG (tHT) for e...

Consider a without replacement sample of size 2 from a population of size 4, with joint inclusion

Question:

Consider a without replacement sample of size 2 from a population of size 4, with joint inclusion probabilities π12 = π34 = 0.31, π13 = 0.20, π14 = 0.14, π23 = 0.03, and π24 = 0.01.
a. Calculate the inclusion probabilities πi for this design.
b. Suppose t1 = 2.5, t2 = 2.0, t3 = 1.1, and t4 = 0.5. Find ṼHT (ˆtHT) and ṼSYG (ˆtHT) for each possible sample.

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