Checking the Accuracy of a Monte Carlo Integration. Use Monte Carlo to estimate

Question

Checking the Accuracy of a Monte Carlo Integration. Use Monte Carlo to estimate the integral theta = integral_2^4 (3x^2 - 2x - 10) dx. Perform this calculation m - 1000 times each for Monte Carlo sample sizes of n - 1000, n = 10,000, and n = 100,000. For each n, plot a histogram of theta_(n)1, ..., theta_(n) and calculate the mean squared error of the estimate, MSE_(n) = 1/m sigma_i = 1^m (theta_(n) i - theta_0) where theta_n)i is the i^th MC estimate of theta for sample size n, and theta_0 is the true value of the integral theta.

Explanation / Answer

The value of integral in three cases is :

Simulations:

value f1 value f2 value f3 38 34.35 33.23

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