Question: Consider the two-way ANOVA:

for \(i=1, \ldots, r, j=1, \ldots, J, k=1, \ldots, K\). Under the assumptions that the errors are independent, mean 0 , finite variance \(\sigma^{2}\). Establish the following properties of the estimators of the parameters:

1. \(E(\bar{y} \ldots)=\mu\)
2. \(E\left(\hat{\alpha}_{1}\right)=\alpha_{1}\)
3. \(E\left((\alpha \beta)_{1,2}\right)=(\alpha \beta)_{1,2}\)
4. \(\operatorname{Var}(\bar{y} \ldots)=\sigma^{2} /(r J K)\)

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