Calculate s-Weights with fixed yields and more

Dear experts,

I have a couple of questions about sWeights.

  1. We are only interested in the weight for the signal. So instead of calculating sWeights with many classes for our many backgrounds we consider only 2 classes: a signal and a total background class. The pdf of the total background is the sum of all single background pdfs (in the right proportions). And they total background yield is the sum of the bkg yields. Is this an equivalent way of calculating sWeights?

  2. Some of our background yields are fixed to known values. In the sPlot paper ( I see c factors are introduced to take fix
    yields into account (eq 72 pay 25). This seems to be absent in the RooStats implementation.
    So my question is: RooStats takes all into account correctly if I fit with some fixed yields but I free them just before the sW calculation?