  Mix-cumulants of conserved charge distributions are sensitive observables for
probing properties of the QCD medium and phase transition in heavy-ion
collisions. To perform precise measurements, efficiency correction is one of
the most important step. In this study, using the binomial efficiency model, we
derive efficiency correction formulas for mutually exclusive and inclusive
variables. The UrQMD model is applied to verify the validity of these formulas
for different types of correlations. Furthermore, we investigate the effect of
the multiplicity loss and contamination emerging from the particle
identifications. This study provides an important step toward future
measurements of mixed-cumulants in relativistic heavy-ion collisions.
