Derive the expected mean squares for a balanced three-stage nested design assuming that a is fixed and that b and c are random. obtain formulas for estimating the variance components. assume the restricted form of the mixed model.

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement