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.vodafone AU WiFi 6 of 9 QUESTION 2 ment 8:54 PM mcpl.moodlesites.com Background Monte Carlo methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. You have been asked to estimate the value of rt using the Monte Carlo method. Itz A number of randomised points is generated within the box of unit width, as shown in figure 2. Some of the points lie within the circle, while others lie outside the circle. The value of it is calculated using the following expression: 4Nc Ng Page 5 of 9 [3 MARKS] Figure 2: Randomised points generated inside a box containing a unit circle. The procedure to perform the Monte Carlo method is listed below: 1. Generate a randomised point within a square containing a circle of unit radius 2. Determine N, and N₁, and calculate the estimate of r 3. Repeat steps 1 and 2 for a specified number of points MCD4140 Assignment where Nc represents the number of points inside the unit circle, and Ns is the number of dots within the square. In figure 1, there are 17 points inside the circle and 20 points inside the square (i.e. 3 points outside the circle). Therefore, 4x17 3.4. This estimated value of should become more accurate with an increasing number of points. 20 Complete the following tasks to perform the Monte Carlo procedure described above. 2% Q2a In the Q2a.m file, generate a 2x1 subplot arrangement where the top panel contains a circle of unit radius and a square with a width of 2 units, both centred at (x,y) = (0,0) (see figure 3 for an example). Plot these shapes as black lines and set the axes to be square (option for axis). Details of the bottom panel are described in Q2b. Page 6 of 9 Q2b In the Q2b.m file, prompt the user for a specified number of points to estimate using the input() function. Generate your first randomised point by randomising its x and y-coordinates. The limits for the x and y- coordinates should be limited to the bounds of the square (i.e. from 1 to 1 in both directions). Plot this randomised point in the top panel of the figure as a red dot if it lies on or within the circle, or as a blue dot if it is outside the circle. Use a marker size of 15. After plotting your first randomised point, calculate the estimate of and plot the result as a black dot in the bottom panel of the figure (see figure 3). The current

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