Consider a random effects model for a two-factor crossed experimental design: Yik = #+A,+ By + (AB)y + Eijk where i = 1, ..., a and j = 1, ..., b and k = 1. ...,n. A, ~ N(0.o)). B, ~ N(0, of ) and Eyk did N(0, ' ). (a) Derive the variance of Y.=4 ). E, Ex Yuk. (b) Derive an unbiased estimator of Var (V...) (c) For an experiment with MS(A) = 17.73, MS(B) = 0.58 and MS(AB) = 0.05 and a = 4,b = 5, n = 2, determine the Satterthwaite approximation to the degrees of freedom associated with the estimated variance of V