We take an analytical approach to study Quality of user Experience (QoE) for video streaming applications. First, we show that random linear network coding applied to blocks of video frames can significantly simplify the packet requests at the network layer and save resources by avoiding duplicate packet reception. Network coding allows us to model the receiver's buffer as a queue with Poisson arrivals and deterministic departures. We consider the probability of interruption in video playback as well as the number of initially buffered packets (initial waiting time) as the QoE metrics. We characterize the optimal trade-off between these metrics by providing upper and lower bounds on the minimum initial buffer size, required to achieve certain level of interruption probability for different regimes of the system parameters. Our bounds are asymptotically tight as the file size goes to infinity.