For the random-effects one-way layout model (Section 9.3.2), show that ???? 0 and ui are as stated

Question:

For the random-effects one-way layout model (Section 9.3.2), show that ????̂

0 and ũi are as stated there (i.e., with the known variances). Show that ũi is a weighted average of 0 and the least squares estimate based on treating u as fixed effects. Give an application for which you would prefer ????̂

0 + ũi to the fixed-effect estimate ȳi.

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