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Removing probability folder (#967)
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SUMMARY.md

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* [Multiplication as a Convolution](contents/convolutions/multiplication/multiplication.md)
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* [Convolutions of Images (2D)](contents/convolutions/2d/2d.md)
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* [Convolutional Theorem](contents/convolutions/convolutional_theorem/convolutional_theorem.md)
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* [Probability Distributions](contents/probability/distributions/distributions.md)
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* [Probability Distributions](contents/probability_distributions/distributions.md)
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* [Tree Traversal](contents/tree_traversal/tree_traversal.md)
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* [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md)
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* [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md)

contents/metropolis/metropolis.md

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# The Metropolis Algorithm
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The [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) method uses random numbers to approximate the area of pretty much any shape we choose.
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The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability/distributions/distributions.md):
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The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability_distributions/distributions.md):
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$$
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P(\mathbf{x}) = \frac{f(\mathbf{x})}{\displaystyle\int_D f(\mathbf{x})d\mathbf{x}},
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P(\mathbf{x}) = \frac{\displaystyle \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right]} {Q},
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$$
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where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability/distributions/distributions.md),
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where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability_distributions/distributions.md),
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$$
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Q = \int_D \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right] d\mathbf{x}.

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