This exercise is about using a Monte Carlo simulation to estimate the value of p. The method uses…

This exercise is about using a Monte Carlo simulation to estimate the value of _. The method uses random points chosen inside the unit square in the 2D Cartesian axes, i.e. 0 _ x _ 1 and 0 _ y _ 1. This is illustrated in the figure below which shows part of the unit circle and random points in the unit square.The method picks random points inside the unit square, and these are shown by dots in the diagram. Some of these points will lie inside the unit circle (which is also plotted) and some of the points will lie outside the unit circle. We can estimate the area of the quarter circle by

»This exercise is about using a Monte Carlo simulation to estimate the value of _. The method uses random points chosen inside the unit square in the 2D Cartesian axes, i.e. 0 _ x _ 1 and 0 _ y _ 1. This is illustrated in the figure below which shows part of the unit circle and random points in the unit square.The method picks random points inside the unit square, and these are shown by dots in the diagram. Some of these points will lie inside the unit circle (which is also plotted) and some of the points will lie outside the unit circle. We can estimate the area of the quarter circle by finding the fraction of points that are inside it. From this, we can estimate the area of the whole circle and therefore the value of _. For example, if we pick 20 points inside the square and 17 turn out to be also inside the unit circle the estimate for the area of the circle (i.e. _) is 4 × 17 ÷ 20 = 3.4. Write MATLAB code to do this. Break the problem down into a number of sub-tasks and use different functions to carry out each sub-task. Use a main function or main script to control the flow of the program. The user should be able to choose how many points are picked and the program should print a suitable output message 

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