title: Understanding the Poisson distribution of a random number generator
body: <p>I'm working with the random number generator available within C++11. At the moment, I'm using a uniform distribution, which should give me an equal probability to get any number within the range A &amp; B which I specify.</p>
  
  <p>However, I'm confused about generating Poisson distributions. While I understand how to determine the <a href="http://stattrek.com/Lesson2/Poisson.aspx?Tutorial=stat">Poisson probability</a>, I don't understand how a random series of numbers can be "distributed" based on the Poisson distribution.</p>
  
  <p>For instance, the C++11 constructor for a Poisson distribution takes one argument -- λ, which is the <a href="http://www.johndcook.com/cpp_TR1_random.html#poisson">mean of the distribution</a></p>
  
  <pre><code>std::tr1::poisson_distribution&lt;double&gt; poisson(7.0);
  std::cout &lt;&lt; poisson(eng) &lt;&lt; std::endl;
  </code></pre>
  
  <p>In a Poisson probability problem, this is equal to the expected number of successes / occurrences during a given interval. However, I don't understand what it represents in this instance. What is a "success" / "occurrence" in a random number scenario?</p>
  
  <p>I appreciate any assistance or reference materials which I can use to help me understand this.</p>