You and your friend go to a Carnival and encounter the following puzzle at one of the game tables. There are 27 red and blue marbles in the bag. The number of red marbles is 5 less than 3 times the number of blue marbles. You are given two minutes to figure the puzzle out, and if you win, you get a giant pink stuffed Panda. A. Write a system of equations for the situation above, then solve the system.

B. How many red marbles are there?

C. How many blue marbles are there?

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) ).