I have the following excercise :
Let C be an Archimedean copula with generator given by $\psi(x) = E[e^{ −xV} ]$, where V is an exponentially distributed random variable with expectation 1. Calculate the probability $P[U_1 > \frac{1}{2}, U_2 > \frac{1}{2}]$ for $(U_1, U_2) \sim C$.
I struggle to start with the solution as I seem to not be able to find a connection between the generator function and the probability. I thought I could maybe get the densities from the copula, but that is also not the case, at least I don't see it. Does someone know how to proceed?
Best