The location of Avenger's Tower is important to the safety of our planet. Steve, Natasha, and Bruce happen to all live equidistant from each other. Since Tony is filthy rich and can buy whatever he wants, he has decided to place the tower somewhere between their houses. Where in this triangle should the tower be located and why? Geometrically, how could you find this spot? (Assume that no super powers
or tech will assist these 3 Avengers when they travel to the tower)

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).