12 Jan 1. Let I = 2 1 e-x2/2 v2p dx. (a) Estimate I usi
1. Let I = 2 1 e-x2/2 v2p dx. (a) Estimate I using the basic Monte Carlo method. Use N = 100, 000. Also, find the estimated standard error. (b) Find an (analytical) expression for the standard error of your estimate in (a). Compare to the estimated standard error. (c) Estimate I using importance sampling. Take g to be N(1.5, v2) with v = .1, v = 1 and v = 10. Compute the (true) standard errors in each case. Also, plot a histogram of the values you are averaging to see if there are any extreme values. (d) Find the optimal importance sampling function g*. What is the standard error using g*?
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