questions 1-4

Obtain the MC estimate of 0 = E X*e 4 I(X > 2) , where X ~ N(0, 1) using the density function of N(#, 1) as an importance sampling density. 1. Estimate O using # = 2. 2. Estimate O using / determined from the Maximum Principle. 3. Calculate the variances of the estimators from 1) and 2). Which estimator is more efficient? 4. Find the 95% CI for 0 using (2)