Consider a random sample \(Y_{1}, \ldots, Y_{N}\) with the exponential
distribution
\\[f\left(y_{i} ; \theta_{i}\right)=\theta_{i} \exp \left(-y_{i}
\theta_{i}\right).\\]
Derive the deviance by comparing the maximal model with different values of
\(\theta_{i}\) for each \(Y_{i}\) and the model with \(\theta_{i}=\theta\) for all
\(i\).
