mmary>Soln. 18.18</summary><p>From (18.53) in the text we obtain</p>
<div class="arithmatex">\[\begin{eqnarray}
    \text{pFDR}(\Gamma) &amp;=&amp; \text{Pr}(Z_j=0|t_j\in \Gamma)\non\\
    &amp;=&amp;\frac{\pi_0\cdot\text{Pr}(t_j\in \Gamma|Z_j=0)}{\pi_0\cdot\text{Pr}(t_j\in \Gamma|Z_j=0) + \pi_1\cdot\text{Pr}(t_j\in \Gamma|Z_j=1)}\non\\
    &amp;=&amp;\frac{\pi_0\cdot \{\text{Type I error of } \Gamma\} }{\pi_0\cdot \{\text{Type I error of } \Gamma\} + \pi_1\cdot\{\text{Power of }\Gamma\}}.\non
\end{eqnarray