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J Unpingco
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Random walks and stumbles
Random walks and random stumbles Random walks are a gold mine for a wide variety of stochastic theory and practice. They are easy to explain, easy to code, and easy to misunderstand. In this section, we start out with the simplest imaginable random walk and...

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Methods of Random Sampling Using Rejection
Introduction We want to generate samples of a given density, $f(x)$. In this case, we can assume we already have a reliable way to generate samples from a uniform distribution, $\mathcal{U}[0,1]$. How do we know a random sample ($v$) comes from the $f(x)$ d...

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Exploring Buffon's Needle Using Python Tools
Buffon's Needle ¶ The problem is to randomly drop a needle on the unit square and count the number of times that the needle touches (or "cuts") the edge of the square. This is a well-studied problem, but instead of the usual tack of going directly for the ...

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Stitching Monte Carlo Methods with Buffon's Needle
Buffon's Needle ¶ The problem is to randomly drop a needle on the unit square and count the number of times that the needle touches (or "cuts") the edge of the square. This is a well-studied problem, but instead of the usual tack of going directly for the ...

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