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For the mean, you can apply the linearity of expectation a bit more aggressively than you do: since this is just a finite sum we know we can exchange expectation and summation so $$ \text E\left(\sum_{ij} Y_{ij}\right) = \sum_{ij} \text E Y_{ij} = nt\mu $$ and then $\text E \bar Y_{++}$ follows. For the variance, the key step is remembering that the random ...


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