Assume a sample on which you are about to conduct a randomized experiment with potential outcomes as indicated in the table below. Assume that for this experiment, you will randomize each of the units below to receive treatment Z = 1 or control Z = 0, and benefit of treatment will be determined on the basis of how much it increases the value of the outcome. Unit, i Assignment, Zi Y. (0) Yi (1 ) 51 71 2 35 45 3 46 56 78 78 5 23 43 45 55 84 84 8 52 72 14 24 10 21 31 Among all possible treatment vectors, which realized treatment vector would yield the largest estimate of the SATE? O (1,0,1,1,0,0,1,1,0,0) O (0,1,0,0,1,1,0,0,1,1) O (1,1,1,1,0,1,1,1,0,0) O (0,0,0,0,1,0,0,0,1,1) O (1,1,1,0,1,1,0,1,1,1) Assuming a Bernoulli randomization with a probability of assignment to treatment of 0.5, what is the probability of the treatment assignment vector that would yield the largest estimate of the treatment effect? Enter your answer out to 8 decimal places. Give the treatment assignment vector in the space of all possible vectors for which exactly seven of the units are treated that, if realized, would yield the largest estimate of the SATE. O (1,0,1,1,0,1,1,1,0,1) (1,1,0,0,1,1,0,1,1,1) O (1,1,1,1,0,1,1,1,0,0) O (0,0,0,1,1,1,1,1,1,1) O (1,1,0,0,1,1,0,1,1,1) Assuming a completely randomized experiment with probability of assignment to treatment equal to 0.7, what is the probability of the treatment assignment vector that would yield the largest estimate of the treatment effect? Enter your answer out to 8 decimal places