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**statmajor** Let $\displaystyle X_{ijk}$ be normal distributed with mean $\displaystyle \mu_{ijk}$ and common variance $\displaystyle \sigma^2$. i = 1,...,a ; j = 1,...,b;k = 1,...,c

Find the variance of $\displaystyle \hat{\alpha_i} = \overline{X}_{i..} - \overline{X}_{...}$

$\displaystyle Var(\hat{\alpha_1}) = Var(\overline{X}_{1..} - \frac{\overline{X}_{1..} + ... + \overline{X}_{a..}}{a})=Var(\frac{(a-1)\overline{X}_{1..} - ... - \overline{X}_{a..}}{a}) =$ $\displaystyle a^{-2}[(a-1)^2 \frac{\sigma^2}{n} + (a-1) \frac{\sigma^2}{n}]$

where n = abc. Then I would multiply it by 'a' to find $\displaystyle Var(\hat{\alpha_i})$ Have I made a mistake somewhere?