34 lines
1.1 KiB
ReStructuredText
34 lines
1.1 KiB
ReStructuredText
Introduction
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==================
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Metrics
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----------------
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* **Expected value/Espérance**: Noted :math:`\mathbb{E}[X]`, is a **theorical value**. For example, when playing coin
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flipping, the expected value for getting heads or tails is 0.5.
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Variance
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^^^^^^^^^^^^^^
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Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`.
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.. math::
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\mathbb{V}[X]=\mathbb{E}[X-\mathbb{E}[X]]^2=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])^2}{n}=\mathrm{Cov}(X,X)
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Covariance
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^^^^^^^^^^^^^^
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Covariance is a way to quantify the relationship between two random variables :math:`X` and
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:math:`Y` (`source <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT**
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quantify how strong this correlation is! If covariance is:
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Positive
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For large values of :math:`X`, :math:`Y` is also taking large values
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Negative
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For large values of :math:`X`, :math:`Y` is also taking low values
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Null
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No correlation
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.. math::
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\mathrm{Cov}(X,Y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])(y_i - \mathbb{E}[Y])}{n}
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