Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 205 / 4 / c / Solution

Under the intersection null, every rejection is false, so the false-discovery proportion is $1_{\{R>0\}}$ 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 thereforeEquivalently, the order-statistic identity in the hint gives the same equality by induction on $m$.