Monte Carlo is an area in the small city-state of Monaco, and it is well known,...

 

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Monte Carlo is an area in the small city-state of Monaco, and it is well known, among others. for its casinos. Because of its association with games of chance, Nicolas Metropolis and Stanislaw Ulam named a class of computational methods that are based on random sampling Monte Carlo methods. The purpose of the assignment is to employ a Monte Carlo method to approximate the value of . We will approximate by generating N random pairs in [0, 1] x [0.1]. The ratio of the number of points in the unit circle (i.e., center at (0,0) and radius= 1) to the total approximates /4. 1. Calculate and the error with respect to the actual value for different N. 2. For two values of N of your choice, make a scatter plot of the random pairs assigning different colors to points inside and outside the unit circle. 3. Based on your numerical experiment, what is the observed rate of convergence of the method Can you comment on the efficiency of the method? Monte Carlo is an area in the small city-state of Monaco, and it is well known, among others. for its casinos. Because of its association with games of chance, Nicolas Metropolis and Stanislaw Ulam named a class of computational methods that are based on random sampling Monte Carlo methods. The purpose of the assignment is to employ a Monte Carlo method to approximate the value of . We will approximate by generating N random pairs in [0, 1] x [0.1]. The ratio of the number of points in the unit circle (i.e., center at (0,0) and radius= 1) to the total approximates /4. 1. Calculate and the error with respect to the actual value for different N. 2. For two values of N of your choice, make a scatter plot of the random pairs assigning different colors to points inside and outside the unit circle. 3. Based on your numerical experiment, what is the observed rate of convergence of the method Can you comment on the efficiency of the method?

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