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For the computation of the expectation Ef [h(X)] when f is the normal pdf and h(x) = exp(-(x - 3)2/2) + exp(-(x - 6)2/2):
a. Show that Ef [h(X)] can be computed in closed form and derive its value.
b. Construct a regular Monte Carlo approximation based on a normal N (0, 1)sample of size Nsim=10^3 and produce an error evaluation.
c. Compare the above with an importance sampling approximation based on an importance function g corresponding to the U(-8, -1) distribution and a sample of size Nsim=10^3.
(Warning: This choice of g does not provide a converging approximation of Ef [h(X)]!)
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