Question: Problem 1 (Conditional Monte Carlo): Consider the following probability 0 = P(X1 + X2 > 8) where X1 ~ Exp(2) and X2 ~ Exp(1). For

Problem 1 (Conditional Monte Carlo): Consider the following probability 0 = P(X1 + X2 > 8) where X1 ~ Exp(2) and X2 ~ Exp(1). For X ~ Exp()), the corresponding CDF is given by F(x) = 1 -e-xx. (a) Use standard simulation to estimate it. (b) Use Conditional Monte Carlo to estimate it. (c) Find approximate 99% confidence intervals in both cases and compare. Use 10,000 draws/samples (You should include your codes and print out the results)

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