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Monte Carlo Procedures for computing areas 9/30

Based on the idea that you can compute an approximation of an area by generating points unifromly at random and looking at the proportion of them that fall within that area.

Here is an applet for trying a Monte Carlo simulation to determine the area under a quadratic curve. http://www.dartmouth.edu/~chance/teaching_aids/probability_book/bookapplets/chapter2/MonteCarlo/MonteCarlo.html

How would one compute an estimate of $\pi$ by such a method?
Method 1: Take points in the unit square, what is the probability that they fall in the inscribed circle?

\begin{displaymath}P(E)=\pi(\frac{1}{2})^2\end{displaymath}



 

Susan Holmes
1998-12-07