On mixture densities in importance sampling

E c SM ( M large), f (n ) = c,\e-A4(n), and X > 0 usually represents a physically meaningful parameter (such as signal-to-noise ratio (SNR) or number of servers in the network, depending on the context) that we will consider to be asymptotically large. Direct Monte Carlo evaluation of (1) is well-known to be inefficient, and Importance Sampling (IS) has established itself as an attractive alternative [l, 41. The Importance Sampling (IS) estimator for ( I ) is