title: Distribution of Random Numbers
body: <p>I have two options of code:</p>
  
  <p><strong>Option 1</strong></p>
  
  <pre><code>int myFunc() {
    return new Random().nextInt();
  }
  </code></pre>
  
  <p>Or:</p>
  
  <p><strong>Option 2</strong></p>
  
  <pre><code>private static final Random random = new Random();
  
  int myFunc() {
    return random.nextInt();
  }
  </code></pre>
  
  <p>I understand that <code>option 2</code> is more idiomatic. I am wondering about the validity of <code>option 1</code>.</p>
  
  <p>In <code>option 1</code> I will only ever use the first number generated by a given seed. In <code>option 2</code> I choose a seed and generate <code>n</code> numbers using that seed. IIUC the guarantees on randomness are on this use case.</p>
  
  <p>My question is, therefore, if I call <code>option 1</code> many times are there any guarantees on the uniformity of the distribution of the output?</p>