Question: 30. Let Xl ' Xn be independently normally distributed with common variance 0 2 and means t = a + Pt; + rt;, where

30. Let Xl" ' " Xn be independently normally distributed with common variance 0 2 and means t = a + Pt; + rt;, where the t, are known. If the coefficient vectors (tt , . . . , t:), k = 0,1,2, are linearly independent, the parameter space TIo has dimension s = 3, and the least-squares estimates

a, /J, y are the unique solutions of the system of equations aLtf + PLtf+1 + YLtf+2 = Ltf~ (k = 0,1,2). The solutions are linear functions of the X's, and if y = Ec;~, the hypothesis Y = 0 is rejected when lyVVLC; YL(~ - a - Pt; - ytt)2/(n - 3

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