maths.joint_probability_distribution
====================================

.. py:module:: maths.joint_probability_distribution

.. autoapi-nested-parse::

   Calculate joint probability distribution
   https://en.wikipedia.org/wiki/Joint_probability_distribution



Attributes
----------

.. autoapisummary::

   maths.joint_probability_distribution.x_vals


Functions
---------

.. autoapisummary::

   maths.joint_probability_distribution.covariance
   maths.joint_probability_distribution.expectation
   maths.joint_probability_distribution.joint_probability_distribution
   maths.joint_probability_distribution.standard_deviation
   maths.joint_probability_distribution.variance


Module Contents
---------------

.. py:function:: covariance(x_values: list[int], y_values: list[int], x_probabilities: list[float], y_probabilities: list[float]) -> float

   >>> covariance([1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2])
   -2.7755575615628914e-17


.. py:function:: expectation(values: list, probabilities: list) -> float

   >>> from math import isclose
   >>> isclose(expectation([1, 2], [0.7, 0.3]), 1.3)
   True


.. py:function:: joint_probability_distribution(x_values: list[int], y_values: list[int], x_probabilities: list[float], y_probabilities: list[float]) -> dict

   >>> joint_distribution =  joint_probability_distribution(
   ...     [1, 2], [-2, 5, 8], [0.7, 0.3], [0.3, 0.5, 0.2]
   ... )
   >>> from math import isclose
   >>> isclose(joint_distribution.pop((1, 8)), 0.14)
   True
   >>> joint_distribution
   {(1, -2): 0.21, (1, 5): 0.35, (2, -2): 0.09, (2, 5): 0.15, (2, 8): 0.06}


.. py:function:: standard_deviation(variance: float) -> float

   >>> standard_deviation(0.21)
   0.458257569495584


.. py:function:: variance(values: list[int], probabilities: list[float]) -> float

   >>> from math import isclose
   >>> isclose(variance([1,2],[0.7,0.3]), 0.21)
   True


.. py:data:: x_vals