Question

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(Monte Carlo) If we are interested in the tail probability Pr(X > 20) when X ~ N (0, 1), simulating from a N(0,1) distribution does not work. Express the probability as an integral and use an obvious change of variable to rewrite this integral as an expectation under a U(0,1/20) distribution. Deduce a Monte Carlo approximation to Pr(X20) along with an error assessment. Compare the performance of this estimator to that of the direct Monte Carlo estimator

Answer 1

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