), \end{eqnarray*}\]</span></p>
</div>
<div id="gradient-of-log-probability-mass-function" class="section level3">
<h3><span class="header-section-number">12.1.3</span> Gradient of Log Probability Mass Function</h3>
<p><span class="math display">\[ \frac{\partial}{\partial \theta} \log \text{Binomial}(n~|~N,\theta)
= \frac{n}{\theta} - \frac{N - n}{1 - \theta} \]</span></p>
</div>
<div id="sampling-statement-3" class="section level3">
<h3><span class="header-section-number">12.1.4</span> Sampling Statement<