In this paper, the outage performance of a dual-hop amplify-and-forward (AF) cooperative diversity system with a maximal-ratio combining receiver at the destination terminal in Rician fading environments with different K-factors is investigated. The signal-to-noise ratio (SNR) at the receiver is upper bounded. Closed-form expressions for the probability density function (PDF) and the moment generating function (MGF) of the bounded SNR are derived. These statistical results are then applied through numerical evaluations to obtain the outage probability. Numerical results of the outage probabilities are presented to illustrate the performance improvement due to cooperative diversity.