# Mixed model with groups with no variability

I am considering the use of mixed models for an analysis of mine, but I may have a concern. Let's take an example from Wikipedia for introducing my question:

Suppose $$m$$ large elementary schools are chosen randomly from among thousands in a large country. Suppose also that $$n$$ pupils of the same age are chosen randomly at each selected school. Their scores on a standard aptitude test are ascertained. Let $$Y_{ij}$$ be the score of the $$j$$th pupil at the $$i$$th school.

With this in mind, consider $$Y_{ij} = \mu + \beta_1 \mathrm{Sex}_{ij} + U_i + W_{ij} \enspace ,$$ where $$\mu$$ is the average test score for the entire population, $$\mathrm{Sex}_{ij}$$ is the dummy variable for boys/girls, $$U_i$$ is the school-specific random effect, and $$W_{ij}$$ is the individual-specific random effect.

My question is: What if there are schools with only boys? Are they excluded from the analysis? Is the school-specific random effect 0 in those cases?