Topological insulators are 3D materials with a band gap in the bulk-electronic structure but with gapless, delocalized, surface states. The most studied topological insulator is Bi2Se3. This material has the simplest band-structure compared to all other topological-insulator systems, its surface state contains a single Dirac fermion mode. Recently superconductivity was found in Cu intercalated Bi2Se3 with a superconducting transition temperature (Tc) of about 4K. We propose to study the superconductivity in the CuxBi2Se3 system using muons. The ultimate aim of this experiment is to combine low energy and bulk muons to disentangle the contribution of the surface and the bulk to the superfluid density to enable the interface properties of a superconductor and topolgical insulator to be tuned.