Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 207 / 1 / c / Solution

Let ${\varphi }_{\rho }$ denote the centered unit-variance bivariate normal distribution density,The complement of rejecting either null hypothesis is $W_1\le c,W_2\le c$. Therefore the probability of at least one rejection isWhen both null hypotheses are true, this is the familywise error rate. If one null hypothesis is false, a rejection of that hypothesis is not a type I error, so the displayed probability is then an any-rejection probability rather than the familywise error rate.