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\[ \begin{array}{lccc} \hline \textbf{True} & \textbf{Non-significant} & \textbf{Significant} & \textbf{Total} \\ \hline \text{No correlation} & U & V (\text{type I error}) & m_0 \\ \text{Correlation} & T (\text{type II error}) & S & m - m_0 \\ \hline \text{Total} & m - R & R & m \\ \hline \end{array} \] \[ Pr(V \ge 1) \\ a^* = 1 - (1-a)^m \] \[ \text{Unobserved random variable} \\ Q=\frac{V}{V+S}=\frac{V}{R} \\ \text{BH focus on the expected Q} \\ E(Q) =E \left(\frac{V}{R}\right) = E(V|R>0) \times P(R>0) \] \[ P_{(i)} \le \frac{i}{m}q^* \]