On the universal distribution of the coverage in split conformal prediction

Two additional universal properties are established in the split conformal prediction framework. In a regression setting with exchangeable data, we determine the exact distribution of the coverage of prediction sets for a finite horizon of future observables, as well as the exact distribution of its almost sure limit. The results hold for finite training and calibration samples, and both distributions are determined solely by the nominal miscoverage level and the calibration sample size.