Unformatted text preview: algorithm and implement it in R based on 1000 samples. Give your estimate and the standard error your estimate. Is this standard error smaller than the one based on the naive Monte Carlo method? Attach your R code. 3. Suppose we want to estimate μ = E ( X 1 { X> 3 . 5 } ), where X has a standard normal distribution and 1 { x> 3 . 5 } is an indicator function. Design an importance sampling algorithm and implement it in R. Give your estimate of μ and the standard error your estimate. Attach the R code. 4. Use importance sampling to estimate σ 2 = E ( X 2 ), where X has the density that is proportional to e x  3 / 3 . Implement your algorithm in R. Give your estimate and the standard error of your estimate based on 1000 samples....
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 Spring '08
 Chen
 Normal Distribution, Standard Error, Monte Carlo method, naive Monte Carlo

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