Response to the following problem:
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(X > 20) along with an error assessment.