Consider the integral G= 2x5dx. (a) Write the integral in the form G= S_96fx[2]dx = E[g(X)]where fx is the density of X-

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Consider The Integral G 2x5dx A Write The Integral In The Form G S 96fx 2 Dx E G X Where Fx Is The Density Of X 1 (128.27 KiB) Viewed 329 times

Consider the integral G= 2x5dx. (a) Write the integral in the form G= S_96fx[2]dx = E[g(X)]where fx is the density of X-U( – 2,1) [2 mark]. Hint 1: none. (b) Find G = E[9(X)] and oʻ(g) = var(g(x)) [4 marks]. Hint 1: none. n (c) Taking n= 105, calculate the Monte Carlo estimate 1 9(Xk) G="{ k= 1 and variance of the Monte Carlo estimator [3 marks]. Hint 1: use the Mathematica functions RandomReals and UniformDistribution or R functions runif and sapply. (d) Using the results from (C), the approximation Gn-G ~N(0,1), vvar(Gn) derive a 95% two-sided confidence interval for G [3 marks].