Statistics Matlab Project : Simulate the Number Pi
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5. 'Simulate the number pi'. Simulate n uniformly distributed random points in the square K={?1<x<1. ?1<y<1}
Determine the number of points, m, that fall into the unit disk x2+y2 < 1. Note that the probability for a random point to be in the unit disk is pi/4. By the law of large numbers we expect m/n converges to pi/4 as n--> oo. Then use 4m/n as an estimate of pi. Plot 4m/n as a function of n and check that it converges to pi as n ?> oo. How big n should be
(give a 'ball park's figure') in order for 4m/n to get within ε = 0.001 from pi? (Use the central limit theorem.)
simulation, modeling, simulating
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The number 'pi' is simulated using Matlab. The solution is detailed and well presented.
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Central Limit Theorem: As sample size increases, the sampling distribution of sample means approaches that of a normal distribution with a mean the same as the population and a standard deviation equal to the standard deviation of the population ...
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