Likelihood function from pdfs


How does ROOT build the likelihood function from the pdfs given to it?

I would like to have a likelihood function written as the product over many bins of:
Poiss(n_i| Nevents_expected(m_i))=Poiss(n_i|Nbkgpdf_bkg(m_i,theta)+Nsigpdf_sig(m_i,theta));
Where n_i is the count of events in the bin centered at mass m_i, Nbkg and Nsig are the total number of background and signal events and theta is the set of nuisance parameters (in addition to Nbkg and Nsig) I’d like to fit.
For instance, pdf_bkg might be a polynomial in the mass and pdf_sig might be a gaussian.

Does this happen automatically when I use pdfs for binned data when I use the FitTo with the LL option?
Do I need to explicitly include the Poisson?


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