Part a: the sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. how many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds? (5 points) part b: which is the more reasonable measurement of the diameter of a human hair: 1.8 ⋅ 10−2 mm or 1.8 ⋅ 102 mm? justify your answer. (5 points)

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) ).