For the balanced block design in the preceding exercise, show that the implied distribution for residuals is a two-parameter full exponential-family model with canonical sufficient statistic \(\mathrm{SS}_{W}, \mathrm{SS}_{B}\). Hence deduce that the residual maximumlikelihood estimate satisfies

\[
\hat{\sigma}^{2}=\mathrm{SS}_{W} /(n-m), \quad 1+b \hat{\theta}=F
\]

Show also that the sub-model with \(\theta=0\) is a one-parameter exponential family model with sufficient statistic \(\mathrm{SS}_{B}+\mathrm{SS}_{W}\).