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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.stat_tut.variates"></a><a class="link" href="variates.html" title="Random Variates and Distribution Parameters">Random Variates and Distribution
  28       Parameters</a>
  29 </h3></div></div></div>
  30 <p>
  31         <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">Random variates</a>
  32         and <a href="http://en.wikipedia.org/wiki/Parameter" target="_top">distribution parameters</a>
  33         are conventionally distinguished (for example in Wikipedia and Wolfram MathWorld
  34         by placing a semi-colon after the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
  35         variate</a> (whose value you 'choose'), to separate the variate from
  36         the parameter(s) that defines the shape of the distribution.
  37       </p>
  38 <p>
  39         For example, the binomial distribution has two parameters: n (the number
  40         of trials) and p (the probability of success on one trial). It also has the
  41         <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random variate</a>
  42         <span class="emphasis"><em>k</em></span>: the number of successes observed. This means the
  43         probability density/mass function (pdf) is written as <span class="emphasis"><em>f(k; n, p)</em></span>.
  44       </p>
  45 <p>
  46         Translating this into code the <code class="computeroutput"><span class="identifier">binomial_distribution</span></code>
  47         constructor therefore has two parameters:
  48       </p>
  49 <pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
  50 </pre>
  51 <p>
  52         While the function <code class="computeroutput"><span class="identifier">pdf</span></code> has
  53         one argument specifying the distribution type (which includes its parameters,
  54         if any), and a second argument for the <a href="http://en.wikipedia.org/wiki/Random_variate" target="_top">random
  55         variate</a>. So taking our binomial distribution example, we would write:
  56       </p>
  57 <pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">);</span>
  58 </pre>
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  62 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  63       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  64       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  65       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  66         Distributed under the Boost Software License, Version 1.0. (See accompanying
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