Question: 4. Consider the random effects model yij = ,u-+O:a: +6135, where a; m N (0, 0'3) and errors are independent with variance Var(.5j) = 02.

4. Consider the random effects model yij = ,u-+O:a: +6135, where a; m N (0, 0'3) and errors are independent with variance Var(.5j) = 02. We assume 55: and 05.5 are independent. (a) Derive the expected value and variance of ya: 1-. (b) Show that Cov(yj,yij:) = 0-3, for j at 5". (c) Show that Cor(y,;J-, my) = J: How can we interpret this correlation? 0% +62 '

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