From 437e9e736a84a2e61c581c1a11db50575bd0a627 Mon Sep 17 00:00:00 2001 From: Loic Guegan Date: Sat, 14 Oct 2023 17:13:16 +0200 Subject: [PATCH] Minor changes --- source/statistics/introduction.rst | 23 ++++++++++++++++++++++- 1 file changed, 22 insertions(+), 1 deletion(-) diff --git a/source/statistics/introduction.rst b/source/statistics/introduction.rst index 0d968fa..295f6b3 100644 --- a/source/statistics/introduction.rst +++ b/source/statistics/introduction.rst @@ -10,4 +10,25 @@ Metrics Variance ^^^^^^^^^^^^^^ -Variance can be seen as the expected squared deviation from the mean of a random variable :math:`X`. +Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`. + +.. math:: + \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) + +Covariance +^^^^^^^^^^^^^^ + +Covariance is a way to quantify the relationship between two random variables :math:`X` and +:math:`Y` (`source `_). Covariance **DOES NOT** +quantify how strong this correlation is! If covariance is: + +Positive + For large values of :math:`X`, :math:`Y` is also taking large values +Negative + For large values of :math:`X`, :math:`Y` is also taking low values +Null + No correlation + +.. math:: + \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} +