Consider the integral e(x+y)2 dxdy a) Estimate the integral using a simple Monte Carlo Method. Find 95% confidence interval for the true value of the integral. b) Estimate the integral I using data generated for a) and applying antithetic variate approach. Find 95% confidence interval for the true value of the integral c) Estimate the integral I using data generated for a) and applying control variate approach. Use as control variate i) Y1 = U + V and ii) Y2 = (U + V)2 . Note that you'll need to calculate exact (theoretical values) of E(K) and E( ) Find 95% confidence interval for the true value of the integral. d) Compare a), b), c). Which variance reduction technique works better here. Consider the integral e(x+y)2 dxdy a) Estimate the integral using a simple Monte Carlo Method. Find 95% confidence interval for the true value of the integral. b) Estimate the integral I using data generated for a) and applying antithetic variate approach. Find 95% confidence interval for the true value of the integral c) Estimate the integral I using data generated for a) and applying control variate approach. Use as control variate i) Y1 = U + V and ii) Y2 = (U + V)2 . Note that you'll need to calculate exact (theoretical values) of E(K) and E( ) Find 95% confidence interval for the true value of the integral. d) Compare a), b), c). Which variance reduction technique works better here