.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/probability/discrete/plot_03_geometric_memoryless.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_probability_discrete_plot_03_geometric_memoryless.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_probability_discrete_plot_03_geometric_memoryless.py:


The geometric distribution: waiting for the first success
=========================================================

The number of independent trials up to and including the first
success, with success probability :math:`p`, has mean :math:`1/p` and is
memoryless: :math:`P(X > m + n \mid X > m) = P(X > n)`.

.. GENERATED FROM PYTHON SOURCE LINES 11-16

.. code-block:: Python

    import numpy as np

    from mathematicskit.probability import Geometric
    from mathematicskit.probability.visualizers.plots import plot_distribution








.. GENERATED FROM PYTHON SOURCE LINES 17-19

Mean = 1/p
------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 19-24

.. code-block:: Python


    geometric = Geometric(p=0.3)
    print(f"geometric(p=0.3) mean = {geometric.mean:.4f}, expected 1/p = {1.0 / 0.3:.4f}")
    plot_distribution(geometric)




.. image-sg:: /api/gallery/probability/discrete/images/sphx_glr_plot_03_geometric_memoryless_001.png
   :alt: Geometric
   :srcset: /api/gallery/probability/discrete/images/sphx_glr_plot_03_geometric_memoryless_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    geometric(p=0.3) mean = 3.3333, expected 1/p = 3.3333

    <Axes: title={'center': 'Geometric'}, xlabel='x', ylabel='P(X = k)'>



.. GENERATED FROM PYTHON SOURCE LINES 25-27

Memorylessness
------------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-32

.. code-block:: Python


    m, n = 4, 3
    conditional = (1.0 - geometric.cdf(m + n)) / (1.0 - geometric.cdf(m))
    print(f"P(X > {m + n} | X > {m}) = {conditional:.4f}, P(X > {n}) = {1.0 - geometric.cdf(n):.4f}")
    print("memoryless:", bool(np.isclose(conditional, 1.0 - geometric.cdf(n))))




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    P(X > 7 | X > 4) = 0.3430, P(X > 3) = 0.3430
    memoryless: True





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.029 seconds)


.. _sphx_glr_download_api_gallery_probability_discrete_plot_03_geometric_memoryless.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_geometric_memoryless.ipynb <plot_03_geometric_memoryless.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_geometric_memoryless.py <plot_03_geometric_memoryless.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_geometric_memoryless.zip <plot_03_geometric_memoryless.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_