2. Use Monte Carlo (MC) to numerically estimate E[g(X)] and put a confidence interval using two SE where SE is MC standa

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2 Use Monte Carlo Mc To Numerically Estimate E G X And Put A Confidence Interval Using Two Se Where Se Is Mc Standa 1 (158.38 KiB) Viewed 20 times

2. Use Monte Carlo (MC) to numerically estimate E[g(X)] and put a confidence interval using two SE where SE is MC standard error. +00 E[g(X)] = [*g(x)f(x)dx -00 where X~Exponential(λ = 0.2) 6X² - 8X g(x) = 5³√x² + 3x + 4X³3X² + 2X - 1 Solution: In R programming Generate a large sample (T= 2000) from Exponential distribution. Calculate T-2000 values for g(x) given the generated sample. Find average of g(X) by averaging calculated g(X)'s. Notice that you have calculated T-2000 g(X)'s. Calculate SE of g(X) using average g(X) and calculated g(x)'s. Use SE of g(x) to find SE of average of g(X). T = 2000 હતની codesofall to rub X = rexp (T,0.2) # gx = write the equation to calculate g(x) meanhat_gX = mean(gX) SEhat_gx = sd(gx) SEhat_meanhat_gX = SEhat_gX /sqrt(T-1) CI_LB = meanhat_gX - 2* SEhat_meanhat_gX CI_UB= meanhat_gX + 2* SEhat_meanhat_gX