This paper proposes a numerical framework to propagate wind-speed uncertainty through to the power output of a wind farm while factoring in the availability of the wind turbines in the farm. In particular, given a probability density function (pdf) that describes wind speed, and a statistical availability model for the wind turbines, we propose a method to determine the wind-farm power output pdf. The proposed framework offers several advantages over conventional methods, e.g., it is agnostic to the wind-speed distribution and easily incorporates wind farm availability. Case studies compare the wind farm power distributions computed using the proposed framework with field data for an actual wind farm. In addition, we demonstrate how the framework allows the computation of common wind generation indices such as the expected available wind energy, expected generated wind energy, and capacity factor.