Solution
= Solution
Under the intersection null, every rejection is false, so the false-discovery proportion is $\mathbf1_{\{R>0\}}$ and its expectation is the <familywise error rate>. Because the p-values are independent and exactly uniform, every super-uniform inequality in part (b) is an equality. Here $|I_0|=m$, and therefore
$$
\mathbb P(R>0)=\operatorname{FDR}=\alpha.
$$
Equivalently, the order-statistic identity in the hint gives the same equality by induction on $m$.