Question

The Monte Carlo (MC) Method (Monte Carlo Simulation) was first published in 1949 by Nicholas Metropolis and Stanislaw Ulam in the work "The Monte Carlo Method" in the Journal of American Statistics Association. The name Monte Carlo has its origins in the fact that Ulam had an uncle who regularly gambled at the Monte Carlo casino in Monaco. In fact, way before 1949 the method had already been extensively used as a secret project of the U.S. Defense Department during the so-called "Manhattan Project". The basic principle of the Monte Carlo Method is to implement on a computer the Strong Law of Large Numbers (SLLN) (see also Lecture 9). The Monte Carlo Method is also typically used as a probabilistic method to numerically compute an approximation of a quantity that is very hard or even impossible to compute exactly like, e.g., integrals (in particular, integrals in very high dimensions!). The goal of Problem 2 is to write a Python code to estimate the irrational number

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