1. In the exercise above, examine the impact of using a truncated exponential distribution Exp(λ) on the variance of the approximation of the tail probability.
2. Given an importance sample (Xi, f(Xi)/g(Xi)), show that if ωi has a Poisson distribution ωi ∼ P(f(Xi)/g(Xi)), the estimator
is unbiased. Deduce that the sample derived by this sampling mechanism is marginally distributed from f.