Chapter 11.1, Problem 14E

To determine

Prove that $E\left({\overline{X}}_{i\cdot }-{\overline{X}}_{\cdot \cdot }\right)={\alpha }_i$ so that ${\widehat{\alpha }}_i={\overline{X}}_{i\cdot }-{\overline{X}}_{\cdot \cdot }$ unbiased estimator for ${\alpha }_i$.