an>. <span class="math display">\[ \text{Binomial}(n~|~N,\theta) = \binom{N}{n}
\theta^n (1 - \theta)^{N - n}. \]</span></p>
</div>
<div id="log-probability-mass-function" class="section level3">
<h3><span class="header-section-number">12.1.2</span> Log Probability Mass Function</h3>
<p><span class="math display">\[\begin{eqnarray*} \log \text{Binomial}(n~|~N,\theta) &amp; = &amp; \log
\Gamma(N+1) - \log \Gamma(n + 1) - \log \Gamma(N- n + 1) \\[4pt] &amp; &amp; {
} + n \log \theta + (N - n) \log (1 - \theta