The Pauli Exclusion Principle (PEP) is a fundamental law in physics, governing the behavior of fermionic particles. The VIP2 Experiment tests this principle with high sensitivity, by search for Pauli-forbidden atomic transitions from the 2p to the 1s shell in copper. The principle of the experiment is to introduce “new” electrons into a copper conductor via a current. The electrons have the possibility to form states with a symmetric component with the atoms of the conductor. These states would violate the Pauli Exclusion Principle. A possible violation is observed by detecting and counting X-rays, originating from the conductor. The transition energy of Pauli-forbidden K X-rays is shifted in energy by 300 eV with respect to the normal K line. This energy difference can be resolved using Silicon Drift Detectors. From the number of photons in the energy region, where the Pauli-forbidden transition is expected, an upper limit for the probability of a violation of the PEP can be calculated. The thesis starts by explaining the physics behind the VIP2 experiment. Subsequently, the experimental setup is discussed, including: Silicon Drift detectors for X-ray detection, scintillators with Silicon photomultiplier readout for active shielding, a cryogenic system for cooling the detectors and a data acquisition system and an experiment control system. The data taken with the described setup in Vienna and in the underground laboratory in Gran Sasso (LNGS) is compared to simulations. The data selection and the detector calibration is described in detail. The final chapter deals with different methods for the analysis of the data taken at LNGS.