Consider a without replacement sample of size 2 from a population of size 4, with joint inclusion probabilities 12 = 34 = 0.31, 13 =

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.