Minor changes

This commit is contained in:
Loic Guegan 2023-10-14 19:21:10 +02:00
parent 70dca12bd6
commit a942bbecfb
2 changed files with 8 additions and 16 deletions

View file

@ -2,10 +2,9 @@ Statistics
=========================
.. toctree::
:maxdepth: 2
:numbered:
:maxdepth: 2
introduction
metrics
dlkdd
sd
Statistics notes.

View file

@ -1,14 +1,11 @@
Introduction
==================
Metrics
----------------
==================
* **Expected value/Espérance**: Noted :math:`\mathbb{E}[X]`, is a **theorical value**. For example, when playing coin
flipping, the expected value for getting heads or tails is 0.5.
Variance
^^^^^^^^^^^^^^
------------------
Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`.
@ -16,7 +13,7 @@ Variance can be seen as the expected squared deviation from the expected value o
\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 <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT**
@ -33,7 +30,7 @@ Null
\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}
Standard deviation
^^^^^^^^^^^^^^^^^^^^^
-----------------------
Standard deviation provides a way to interprete the variance using the unit of :math:`X`.
@ -42,7 +39,7 @@ Standard deviation provides a way to interprete the variance using the unit of :
Standard Error of the Mean
^^^^^^^^^^^^^^^^^^^^^^^^^^^
-----------------------------
Standard Error of the Mean (SEM) quantifies the error that is potentially made when computing the mean.
@ -72,7 +69,3 @@ Output example:
----- Experiment 3 -----
Means SD: 1.27
SEM 1.26
Degree of freedom
-------------------