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We soon expect collisions at the LHC, and will use real data from "random" events to measure these backgrounds, and directly include simulated events "overlaid" on top of the real data background events. Your job would be to study the results of these overlaid data/MC events to help verify that the simulation is doing things correctly, and to compare the real data to simulated backgrounds, for instance.Another possible project is to study additional MC generators, such as DPMJET3, and study what they predict for very far forward interactions of pp colision products with the beampipe and the resulting effects on the cavern haze backgrounds, etc
In addition, you can study a physics analysis that uses muons, such as the "lepton-jets" search, to see the effect of real beam-halo background, for example. What is learned there could then be used by many others in their analyses.