.. _sphx_glr_api_gallery_probability_discrete:

Discrete distributions
------------------------

The problem of points (binomial tails), Poisson's law of rare events,
and the geometric distribution.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Two players stake equal amounts on a game of fair rounds; the first to win a set number of rounds takes the pot. The game is interrupted when player A still needs a wins and player B needs b. How should the pot be split?">

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  .. image:: /api/gallery/probability/discrete/images/thumb/sphx_glr_plot_01_problem_of_points_thumb.png
    :alt:

  :doc:`/api/gallery/probability/discrete/plot_01_problem_of_points`

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      <div class="sphx-glr-thumbnail-title">Pascal and Fermat's problem of points: dividing the stakes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Many independent trials, each with a tiny chance of success, produce a number of successes that follows a Poisson distribution. Poisson (1837) obtained it as the limit of \mathrm{Binomial}(n, p) with n \to \infty, p \to 0 and the mean np = \mu held fixed:">

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  .. image:: /api/gallery/probability/discrete/images/thumb/sphx_glr_plot_02_poisson_rare_events_thumb.png
    :alt:

  :doc:`/api/gallery/probability/discrete/plot_02_poisson_rare_events`

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      <div class="sphx-glr-thumbnail-title">Poisson's law of rare events: the binomial limit</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The number of independent trials up to and including the first success, with success probability p, has mean 1/p and is memoryless: P(X &gt; m + n \mid X &gt; m) = P(X &gt; n).">

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  .. image:: /api/gallery/probability/discrete/images/thumb/sphx_glr_plot_03_geometric_memoryless_thumb.png
    :alt:

  :doc:`/api/gallery/probability/discrete/plot_03_geometric_memoryless`

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      <div class="sphx-glr-thumbnail-title">The geometric distribution: waiting for the first success</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/probability/discrete/plot_01_problem_of_points
   /api/gallery/probability/discrete/plot_02_poisson_rare_events
   /api/gallery/probability/discrete/plot_03_geometric_memoryless