Question attached as image:

Let q E R and consider it : IP(X > q) for X ~ F with density f on R. a) Derive the crude Monte Carlo estimator [LEO of it based on X17 . . . ,Xn i251 F. b) Compute Varmfc) in terms of H. c) Provide the importance sampling estimator for ,u, based on the IS density Mas) = /\\e_M$_Q), a: > g, with parameter /\\ > 0. d) Explain intuitively Why this helper function may lead to an estimator with smaller variance than the crude Monte Carlo estimator? e) Suppose the variance of the importance sampling estimator is 5 - 104. How large is the variance reduction factor of this importance sampling estimator with respect to the crude Monte Carlo estimator at most