Sensor fusion is commonly used to improve the detection and recognition performance of a pattern recognition system. In this paper we propose a prediction model to predict the performance of a sensor fusion system. In particular, we answer two questions associated with the performance prediction in a sensor fusion system: (a) Given the characteristics of the individual sensors how can we predict the performance of the fusion system? (b) How good the prediction is? We provide the Cramer-Rao bounds for the prediction model. We carry out experiments on the publicly available database XM2VTS that has speech and face data.