Transcription of Monte Carlo Methods - MIT
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Monte Carlo Methods - MIT
chapter 17 Monte Carlo Methods59 A taste of Monte Carlo methodMonte Carlo Methods is a class of numerical Methods that relies on random sampling. For example, the followingMonte Carlo method calculates the value of :1. Uniformly scatter some points over a unit square[0,1] [0,1], as in Figure ??.2. For each point, determine whether it lies inside the unit circle, the red region in Figure ??.3. The percentage of points inside the unit circle is an estimate of the ratio of the red area and the area of the square,which is /4. Multiply the percentage by 4 to estimate .The following Matlab script performs the Monte Carlo calculation:1n = 1000000; # number of Monte Carlo samples2x = rand(n, 1); # sample the input random variable x3y = rand(n, 1); # sample the input random variable y4isInside = (x. 2 + y. 2 < 1); # is the point inside a unit circle?5percentage = sum(isInside) / n; # compute statistics: the inside percentage6piEstimate = percentage*4 Exercise each value ofn=100,n=10000 andn=1000000, run the script 3 times.
Chapter 17 Monte Carlo Methods 59 A taste of Monte Carlo method Monte Carlo methods is a class of numerical methods that relies on random sampling. For example, the following ... 60 Monte Carlo method in Engineering: Colloid thruster In many engineering problems, the inputs are inheriently random. As an example of Monte Carlo method for these
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