= Solution
Conditionally on the school effect, the response variance is $\widehat\sigma^2=1.6531$. Marginally,
$$
\widehat{\operatorname{Var}}(\operatorname{THK}_{ij})
=\widehat\tau^2+\widehat\sigma^2
=0.0437+1.6531,
$$
and two distinct students in the same school have estimated covariance $0.0437$.
There is no single coefficient estimate for the random effect because the 28 school deviations are modeled as draws from a mean-zero distribution. The summary reports the estimated distributional variance; individual empirical Bayes predictions can be extracted separately.
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