Consider an RBD with 5 replications and 4 treatments $\displaystyle t_1,t_2,t_3,t_4$. We are given the following three treatment-contrasts:

$\displaystyle \frac{t_1-t_2}{\sqrt{2}}$

$\displaystyle \frac{t_1+t_2-2t_3}{\sqrt{6}}$

$\displaystyle \frac{t_1+t_2+t_3-t_4}{\sqrt{12}}$

Find the covariances of all possible pairs of BLUEs and variances of the BLUEs of the three contrasts.

What I can see is they are mutually orthogonal. Then?