Using the Mplus short course notes (from 5/17/10; slide 96), I can see the equations for calculating the estimated estimated means using covariates, but not the estimated conditional variance. So, the estimated mean for the intercept factor would would just be:
E(eta_0) = intercept + gamma*E(x)
After searching the message boards, looking through the technical appendices, and the short course notes, I can't seem to find the (scalar) formula for the variance of eta_0 once covariates are added. I realize this can be done rather straightforwardly using the TECH4 option, but was wondering if it could be hand calculated from different pieces of the output Mplus provides.