QUESTION 3. To estimate 0 = P(X> a), we can use the importance sampling estimator 72 Ô¸ = = = = f(x + a), n i=1 where Y₁,...,Y ~iid. Exp(X) and

f() is the p.d.f. of X. Now, suppose that X~ N(μ, o²), i.e., 1 2T0 (15 marks) exp (-(*₂μ)²). 20² f(x)= Assume that a > μ+ 1. Determine A that controls the variance of , and give the corresponding upper bound of Var(,), in terms of n, μ, o, a, 0. (Note that for simplicity, you do not need to check the second-order optimality con- dition of the optimizations.)