science-notes/source/statistics/notations.rst

Notations
---------------

This page was inspired from the following `Wikipedia page <https://en.wikipedia.org/wiki/Notation_in_probability_and_statistics>`_.


Sample and Population
=====================

A *population* is the entire population that you want to analyze. It is a exhaustive set. A *sample* is a subset of the population. It is a non-exhaustive set.

.. figure:: figures/population_sample.svg
    :align: center
    :width: 300px

*Statistics* allows you to infers properties on a population using samples with a certain degree of confidence.

Notation: Tale of Schizophrenia
================================
Two different notation conventions are used. The one to use depends if you are working on a *population* or a *sample*:

.. list-table:: Notation
    :align: center
    :header-rows: 1

    * - Metric
      - Population
      - Sample
    * - Sample mean
      - :math:`\mu`
      - :math:`\overline{x}`
    * - Variance
      - :math:`\sigma^2`
      - :math:`s^2`
    * - Standard deviation
      - :math:`\sigma`
      - :math:`s`

Operators
==========

Var esperance etc.. + remove in metrics esperence