Let \(y_{i k}\) be a continuous outcome for the \(k\) th instrument from the \(i\) th subject \((1 \leq i \leq\) \(n, 1 \leq k \leq K)\). Assume that \(y_{i k}\) follows the LMM in (10.11). Let \(y_{i \infty}=\mu+\lambda_{i}\). Show

(a) \(ho_{I C C}=ho_{1}=\operatorname{Corr}\left(y_{i k}, y_{i l}\right)\) is a constant independent of \(k\) and \(l(k eq l)\).

(b) \(p_{1}=\operatorname{Corr}\left(y_{k}, y_{i \infty}\right)=\sqrt{ho_{1}}\).