Bestimmung des Wirkungsquerschnittes der Reaktion $e^+ e^- \to W^+ W^- \to \bar{\ell}\nu \ell \bar{\nu}$

In this diploma thesis the cross-section of the process $e^+ e^- \to W^+ W^- \to \bar{\ell}\nu \ell \bar{\nu}$ is determined at two centre of mass energies. A point of main eort is the investigation of the so called random background. This is done by using the data from the detector ALEPH collected at a centre of mass energy of 189 GeV in 1998 and 196 GeV in 1999. The signal events are selected by using a cut-selection as well as by using a linear discriminant meth