Conditional LM test for serial correlation assuming random individual effects. For \(H_{4}^{b}: ho=0\) (given \(\sigma_{\mu}^{2}>0\) ),

(a) Derive the score, the information matrix, and the LM statistic for \(H_{4}^{b}\).

(b) Verify that for \(H_{4}^{a} ; \lambda=0\) (given \(\sigma_{\mu}^{2}>0\) ), one obtains the same LM statistic as in part (a).